Grade 12 Derivatives Worksheet

This worksheet covers fundamental concepts and applications of derivatives for Grade 12 Calculus students.

Grade 12 Math CalculusDerivatives

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2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.B.4CCSS.MATH.CONTENT.HSF.IF.B.6CCSS.MATH.CONTENT.HSF.BF.B.3

Topics

CalculusDerivativesGrade 12Math

7 sections · Free to use · Printable

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Grade 12 Derivatives Worksheet

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Read each question carefully and show all your work. Simplify your answers where possible.

1. Find the derivative of the following functions:

a) f(x) = 3x^4 - 2x^2 + 5x - 1

b) g(x) = sin(x) + cos(x)

c) h(x) = e^x * x^3

2. What is the derivative of f(x) = (2x + 1)^3?

3(2x+1)^2

6(2x+1)^2

6x(2x+1)^2

3(2x+1)^2 * 2x

3. The derivative dy/dx of the equation x^2 + y^2 = 25 is .

4. If e^(xy) = x - y, then dy/dx is .

5. Find the equation of the tangent line to the curve y = x^3 - 2x + 1 at x = 2.

6. A particle's position is given by s(t) = t^3 - 6t^2 + 9t, where t is in seconds and s is in meters. Find the velocity and acceleration of the particle at t = 2 seconds.

7. The derivative represents the instantaneous rate of change of a function.

True

False