Calculus Lowersixth Science Mathematics

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Differentiation essentials for beginners

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Calculus Lowersixth Science Mathematics


Froggy Jumps Calculus Lowersixth Science MathematicsOnline version Differentiation essentials for beginners by YAKILI LMS 1 What does it mean for a function to be differentiable at a point? a The derivative exists at that point b The function is linear there c The function is continuous there 2 The gradient of a curve at a point represents? a Average rate of change over interval b Slope of the tangent c Area under the curve 3 Differentiation from first principles uses? a Summation of values b Integral of the function c Limit of difference quotient 4 Which rule gives derivative of sin(x)? a d/dx sin x = -cos x b d/dx sin x = cos x c d/dx sin x = sin x 5 Which rule is used to differentiate e^x? a d/dx e^x = e^x b d/dx e^x = e^(-x) c d/dx e^x = x e^x 6 Derivative of a constant is? a undefined b 0 c 1 7 The power rule states d/dx x^n equals? a n x^(n-1) b x^(n+1) c n x^n 8 Derivative of a sum is? a Derivative of product b Sum of derivatives c Derivative of individual terms only 9 Derivative of f(x)=x^3 at x=2 is? a 9 b 6 c 12 10 d/dx (a constant times function) equals? a Derivative of constant b Constant times derivative c Zero 11 What is the derivative of y = 2x? a 2 b 0 c x 12 Differentiability at a point requires function to be? a Discontinuous b T continuous and have a finite slope c Second derivative exists 13 Derivative of ln x is? a 1/x b x c 1/x^2 14 Which rule differentiates f(x) = x^n when n is a real number? a Power rule b Product rule c Chain rule 15 If f'(x) = 0 at a point, the function is? a Maximum value b Vertical tangent c Horizontal tangent 16 Which statement is true about the gradient of a curve? a It is always constant b It equals dx/dy c It equals dy/dx at that point 17 Which is NOT a differentiation rule? a Constant multiple rule b Power rule c Integrating the function 18 Derivative of y = x^0 is? a 1 b 0 c x 19 If f(x)=x^n, then f'(x) = ? a (n+1) x^n b x^(n-1) c n x^(n-1) 20 Rule for derivative of a constant c is? a 0 b 1 c c 21 The derivative of x^2 is? a 2x b x^2 c 2 22 Differentiation at a point requires the function to be? a Negative everywhere b Defined and smooth there c Discontinuous 23 Derivative of e^(2x) is? a e^(2x) b 2x e^(2x) c 2 e^(2x) 24 D/dx(a f(x)) equals? a f'(a x) b a f'(x) if a constant c f'(x)/a 25 What is the derivative of f(x)=cos x? a sin x b -sin x c -cos x 26 Which of these is a differentiability condition? a The function must be periodic b No sharp corners at the point c The function must be increasing 27 If f'(x) exists for all x in interval, f is? a Constant on interval b Undefined on interval c Differentiable on that interval 28 Derivative of y = sqrt(x) is? a 2 sqrt(x) b 1/x c 1/(2 sqrt(x)) 29 Which is not a differentiation rule? a Quotient rule b Chain rule c Disintegration rule 30 Derivative of y = tan x is? a cos x b sec^2 x c csc^2 x 31 First principles define derivative as? a Sum of f values b Limit of [f(x+h)-f(x)]/h c Integral of f 32 If derivative is negative, the function is? a Decreasing b Constant c Increasing 33 Derivative of y = x^n at x=0 for n>1 is? a 0 b n c 1 34 The gradient of a curve at a point is the slope of? a The tangent line b The normal line c The secant line 35 Derivative of ln(x^2) is? a 2/x b 2x c 1/x 36 Which concept is about instantaneous rate of change? a Limit b Integral c Derivative 37 Derivative of f(x)=1/x is? a -1/x^2 b 1/x c 1/x^2 38 Which rule applies to f(g(x)) differentiation? a Chain rule b Quotient rule c Product rule 39 If f'(x)=0 for all x, f is? a Linear b Quadratic c Constant 40 Derivative of y = a^x is? a a x^(a-1) b ln a x c a^x ln a 41 The derivative at a point is undefined if? a Derivative equals zero b Left and right limits differ c Function undefined 42 Which is the derivative of y = x^n when n=0? a 0 b x c 1 43 Derivative of y = x^1 is? a 1 b 0 c x 44 The gradient of a curve at a point is numeric value of? a dx/dy at that point b y value c dy/dx at that point 45 Differentiation from first principles begins with? a Area under curve b Definition of derivative c Function composition 46 Which function has derivative 1 at all x? a f(x)=x+c b f(x)=x^2 c f(x)=e^x 47 Derivative of f(x)=\|x\| at x>0 is? a 1 b 0 c -1 48 Which operation does not change derivative rule? a Adding a constant b Multiplying by x c Changing variable 49 Derivative of y = x^n for n=3 is? a x^2 b 9x c 3x^2 50 What is the derivative of x at x? a 1 b 0 c x

Calculus Lowersixth Science Mathematics

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Calculus Lowersixth Science MathematicsOnline version

by YAKILI LMS

What does it mean for a function to be differentiable at a point?

The gradient of a curve at a point represents?

Differentiation from first principles uses?

Which rule gives derivative of sin(x)?

Which rule is used to differentiate e^x?

Derivative of a constant is?

The power rule states d/dx x^n equals?

Derivative of a sum is?

Derivative of f(x)=x^3 at x=2 is?

d/dx (a constant times function) equals?

What is the derivative of y = 2x?

Differentiability at a point requires function to be?

Derivative of ln x is?

Which rule differentiates f(x) = x^n when n is a real number?

If f'(x) = 0 at a point, the function is?

Which statement is true about the gradient of a curve?

Which is NOT a differentiation rule?

Derivative of y = x^0 is?

If f(x)=x^n, then f'(x) = ?

Rule for derivative of a constant c is?

The derivative of x^2 is?

Differentiation at a point requires the function to be?

Derivative of e^(2x) is?

D/dx(a f(x)) equals?

What is the derivative of f(x)=cos x?

Which of these is a differentiability condition?

If f'(x) exists for all x in interval, f is?

Derivative of y = sqrt(x) is?

Which is not a differentiation rule?

Derivative of y = tan x is?

First principles define derivative as?

If derivative is negative, the function is?

Derivative of y = x^n at x=0 for n>1 is?

The gradient of a curve at a point is the slope of?

Derivative of ln(x^2) is?

Which concept is about instantaneous rate of change?

Derivative of f(x)=1/x is?

Which rule applies to f(g(x)) differentiation?

If f'(x)=0 for all x, f is?

Derivative of y = a^x is?

The derivative at a point is undefined if?

Which is the derivative of y = x^n when n=0?

Derivative of y = x^1 is?

The gradient of a curve at a point is numeric value of?

Differentiation from first principles begins with?

Which function has derivative 1 at all x?

Derivative of f(x)=|x| at x>0 is?

Which operation does not change derivative rule?

Derivative of y = x^n for n=3 is?

What is the derivative of x at x?