Differentiation Rules

Concept Quizzes

Rules of Differentiation warmup
Differentiation - Power Rule
Differentiation - Product Rule
Differentiation - Quotient Rule
Chain Rule
Differentiation of Inverse Functions
Applying Differentiation Rules to Trigonometric Functions
Applying Multiple Differentiation Rules
Differentiation Rules Warmup
Differentiation Rules Problem Solving

Challenge Quizzes

Differentiation Rules: Level 2 Challenges
Differentiation Rules: Level 3 Challenges

Applying Differentiation Rules to Trigonometric Functions

If the derivative of $y=\sin^{-1} (x^2-4)$ can be expressed as $\frac{2x}{\sqrt{f(x)}},$ what is $f(x)?$

-x^2+4

x^2-4

-x^4+8x^2-15

-x^4+4x^2-16

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by Brilliant Staff

If the instantaneous rate of change of $y=\tan^{-1} \frac{x-1}{x+1}$ at $x=23$ is $a,$ what is the value of $\frac{1}{a}?$

527 529 531 530

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by Brilliant Staff

If $2x = \sin^{-1} \frac{192}{208}$ , the rate of change of $y = \sin x \cos x$ can be expressed as $\frac{a}{b}$ , where $a$ and $b$ are coprime integers. What is $a+b$ ?

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by Brilliant Staff

If the derivative of $y=\cos^{-1} (6-6x)$ can be expressed as $\frac{6}{\sqrt{f(x)}},$ what is $f(x)?$

-6+6x

-36x^2+72x-35

6-6x

36x^2-72x+35

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by Brilliant Staff

What is the derivative of $y=3\sin^{4} x?$

12 \sin x

12 \sin^{3} x \cos x

12 \cos^{3} x

12 \sin^{3} x

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by Brilliant Staff

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