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Trigonometry

Find derivatives for the functions in Exercises 15–18. Assume a, b, c, and k are constants.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Find derivatives for the functions in Exercises 15–18. Assume a, b, c, and k are constants.

Expert Solution

Step 1

Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

Given:

The function is $z = \sin^{3} θ$ .

Formula used:

Chain rule of differentiation:

The derivative of composite function $f (g (x))$ is $f' (g (x)) \times g' (x)$ .

Power rule of differentiation:

$(x^{n})' = n \times (x^{n - 1})$

The derivatives of $\sin θ$ is $\cos θ$ .

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