Derivatives Challenge: Grade 12

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Derivatives quiz for grade 12

Created by

Noor Alzoubi

United Arab Emirates

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Derivatives Challenge: Grade 12Online version Derivatives quiz for grade 12 by Noor Alzoubi 1 What is the derivative of f(x)=x^3? a x^2 b 3x^2 c 9x d 3x 2 Differentiate (3x^2+5)^4 with respect to x. a (3x^2+5)^4 b 12x(3x^2+5)^2 c 24x(3x^2+5)^3 d 6x(3x^2+5)^3 3 Using the product rule, derivative of f(x)=x^2·sin x is? a 2x cos x b x^2 sin x + 2x cos x c sin x + x^2 d 2x sin x + x^2 cos x 4 Derivative of (x)/(x^2+1) by quotient rule? a (1 - x^2)/(x^2+1)^2 b (x^2-1)/(x^2+1)^2 c (x^2+1+2x^2)/(x^2+1)^2 d (1+x^2)/(x^2+1)^2 5 Derivative of ln x (x>0) is? a ln x / x b 1/x c 1/x^2 d x 6 Second derivative of f(x)=x^3 is? a 6x^2 b 6x c 9x d 3x^2 7 Derivative of e^{ax} with respect to x is? a e^{ax} b ae^{x} c a e^{ax} d a^x 8 Implicit differentiation: from x^2 + y^2 = 4, dy/dx equals? a -x^2/y b -2x/y c -y/x d -x/y 9 For f(x)=-x^2+4x, the critical point occurs at x= ? a 4 b 2 c -2 d 0 10 If y = x^3, slope of its inverse at y=8 is? a 1/12 b 3/8 c 1 d 2/3

Derivatives Challenge: Grade 12Online version

Derivatives quiz for grade 12

by Noor Alzoubi

What is the derivative of f(x)=x^3?

x^2

3x^2

Differentiate (3x^2+5)^4 with respect to x.

(3x^2+5)^4

12x(3x^2+5)^2

24x(3x^2+5)^3

6x(3x^2+5)^3

Using the product rule, derivative of f(x)=x^2·sin x is?

2x cos x

x^2 sin x + 2x cos x

sin x + x^2

2x sin x + x^2 cos x

Derivative of (x)/(x^2+1) by quotient rule?

(1 - x^2)/(x^2+1)^2

(x^2-1)/(x^2+1)^2

(x^2+1+2x^2)/(x^2+1)^2

(1+x^2)/(x^2+1)^2

Derivative of ln x (x>0) is?

ln x / x

1/x

1/x^2

Second derivative of f(x)=x^3 is?

6x^2

3x^2

Derivative of e^{ax} with respect to x is?

e^{ax}

ae^{x}

a e^{ax}

a^x

Implicit differentiation: from x^2 + y^2 = 4, dy/dx equals?

-x^2/y

-2x/y

-y/x

-x/y

For f(x)=-x^2+4x, the critical point occurs at x= ?

-2

If y = x^3, slope of its inverse at y=8 is?

1/12

3/8

2/3

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Derivatives Challenge: Grade 12

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About this activity

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Derivatives Challenge: Grade 12Online version

by Noor Alzoubi

What is the derivative of f(x)=x^3?

Differentiate (3x^2+5)^4 with respect to x.

Using the product rule, derivative of f(x)=x^2·sin x is?

Derivative of (x)/(x^2+1) by quotient rule?

Derivative of ln x (x>0) is?

Second derivative of f(x)=x^3 is?

Derivative of e^{ax} with respect to x is?

Implicit differentiation: from x^2 + y^2 = 4, dy/dx equals?

For f(x)=-x^2+4x, the critical point occurs at x= ?

If y = x^3, slope of its inverse at y=8 is?

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