Limits & Differentiation Limits of Functions Lowersixth Science Mathematics

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Short questions on basic differentiation rules.

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Limits & Differentiation Limits of Functions Lowersixth Science Mathematics


Froggy Jumps Limits & Differentiation Limits of Functions Lowersixth Science MathematicsOnline version Short questions on basic differentiation rules. by YAKILI LMS 1 What is d/dx of a constant c? a 0 b 1 c c 2 Differentiate y = c, where c is constant. a 0 b c c 1 3 Find d/dx of y = 5. a 0 b 5 c 1/5 4 d/dx of y = 3x is a 3 b x c 0 5 Derivative of y = 2x is a 4 b 2 c x 6 d/dx (ax) where a is constant equals a ax b a c 1 7 Derivative of f(x)=kx is a 1/k b kx c k 8 Derivative of x^n is a 1/n x^(n-1) b n x^(n-1) c x^(n+1) 9 d/dx of x^3 a 3x^2 b 3x c x^2 10 Derivative of sin(x) is a cos(x) b -cos(x) c -sin(x) 11 Derivative of cos(x) is a sin(x) b -sin(x) c cos(x) 12 Derivative of e^x a x e^(x-1) b e^x c ln(e^x) 13 Derivative of ln(x) is a 1/x^2 b 1/x c x 14 d/dx (f+g) equals a fg' + gf' b f' + g' c f' g' 15 d/dx (f - g) equals a f' + g' b f' - g' c f g' - g' 16 d/dx (c f(x)) where c is constant a c f'(x) b c f(x) c f'(cx) 17 Product rule: d/dx [u(x)v(x)] a u v' + u'v' b u'v + uv' c u'v' + uv 18 If y = u v, dy/dx = a u'v' + uv' b u'v + uv' c u v' - u'v 19 Product rule reduces to? when v is constant a u'v b u v' c u' v' 20 Derivative of reciprocal: d/dx (1/u) = a u'/u^2 b u^2/u' c -u'/u^2 21 d/dx [1/u] equals a -u'/u^2 b -u/u^2 c u'/u^2 22 Derivative of 1/x is a 1/x^2 b -1/x^2 c 1/x 23 If f(x) = x^2, f'(x) = a x^2 b 2x c x 24 Derivative of x^0 is a x b 0 c 1 25 d/dx (ax^2) = a a^2x b 2x^2 c 2ax 26 Derivative of a sum: (x^2 + x)' a 2x + 1 b 2x - 1 c x^2 + x 27 Derivative of a difference: (x^3 - x)' a 3x^2 + 1 b 3x^2 - 1 c x^3 - x 28 Derivative of y = ax^3 is a 3x^3 b a^3x^2 c 3ax^2 29 Which is derivative of kx^4? a kx^3 b 4kx^3 c 4x^4 30 d/dx [sin(2x)] a -2cos(2x) b cos(2x) c 2cos(2x) 31 d/dx [cos(3x)] a -3sin(3x) b 3sin(3x) c -3cos(3x) 32 d/dx of tan(x) is a sec^2(x) b cos^2(x) c sec(x) 33 Derivative of cot(x) is a -sec^2(x) b -csc^2(x) c csc^2(x) 34 If f(x)=x^-1, f'(x) = a x^-2 b -x^-2 c 2x^-1 35 Derivative of a function at a point is the a second derivative b instant rate of change c average rate of change 36 d/dx (ln x^2) = a 2x b 2/x c 1/x 37 d/dx [log_a x] = a a/x b ln(a)/x c 1/(x ln a) 38 Derivative of e^(3x) is a 3e^(3x) b e^(9x) c e^(x) 39 Derivative of a constant times f(x) is a f'(cx) b c f'(x) c c' f(x) 40 d/dx [f(x)g(x)h(x)] is a f'g'h' b sum of products with + c product of derivatives 41 d/dx (x*y) if y is constant w.r.t x a 0 b x c y 42 Derivative of x^n at n=0 is a 0 b n c 1 43 d/dx [a + b x] where a,b constants a a b b c ab 44 If f(x)=x^2, slope at x=1 is a 4 b 2 c 1 45 Derivative of y = x^2 - 4x + 7 is a 2x - 4 b x - 7 c 2x + 4 46 d/dx (4x^3 - x) = a 4x^2 - 1 b 12x^2 + 1 c 12x^2 - 1 47 Derivative of an exponential form a^x is a a^x ln a b x a^(x-1) c ln a^x 48 d/dx [arbitrary function f(x)'] a f''(x) b f'(x) c f(x) 49 Derivative of y = sqrt(x) is a 2 sqrt(x) b 1/x c 1/(2 sqrt(x)) 50 Derivative of y = x^(1/2) is a 1/x b 2 sqrt(x) c 1/(2 sqrt(x))

Limits & Differentiation Limits of Functions Lowersixth Science Mathematics

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Limits & Differentiation Limits of Functions Lowersixth Science MathematicsOnline version

by YAKILI LMS

What is d/dx of a constant c?

Differentiate y = c, where c is constant.

Find d/dx of y = 5.

d/dx of y = 3x is

Derivative of y = 2x is

d/dx (ax) where a is constant equals

Derivative of f(x)=kx is

Derivative of x^n is

d/dx of x^3

Derivative of sin(x) is

Derivative of cos(x) is

Derivative of e^x

Derivative of ln(x) is

d/dx (f+g) equals

d/dx (f - g) equals

d/dx (c f(x)) where c is constant

Product rule: d/dx [u(x)v(x)]

If y = u v, dy/dx =

Product rule reduces to? when v is constant

Derivative of reciprocal: d/dx (1/u) =

d/dx [1/u] equals

Derivative of 1/x is

If f(x) = x^2, f'(x) =

Derivative of x^0 is

d/dx (ax^2) =

Derivative of a sum: (x^2 + x)'

Derivative of a difference: (x^3 - x)'

Derivative of y = ax^3 is

Which is derivative of kx^4?

d/dx [sin(2x)]

d/dx [cos(3x)]

d/dx of tan(x) is

Derivative of cot(x) is

If f(x)=x^-1, f'(x) =

Derivative of a function at a point is the

d/dx (ln x^2) =

d/dx [log_a x] =

Derivative of e^(3x) is

Derivative of a constant times f(x) is

d/dx [f(x)g(x)h(x)] is

d/dx (x*y) if y is constant w.r.t x

Derivative of x^n at n=0 is

d/dx [a + b x] where a,b constants

If f(x)=x^2, slope at x=1 is

Derivative of y = x^2 - 4x + 7 is

d/dx (4x^3 - x) =

Derivative of an exponential form a^x is

d/dx [arbitrary function f(x)']

Derivative of y = sqrt(x) is

Derivative of y = x^(1/2) is