Answered: 37. у 3D 8

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 51E

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Question

Derivatives Find the derivative of the following functions

Expert Solution

Step 1

We have to find the derivative of the function:

$y = 8^{x}$

Solving by logarithmic method,

taking $\ln ()$ both sides,

$\begin{array}{rcl} y & = & 8^{x} \\ \ln (y) & = & \ln (8^{x}) \\ \ln (y) & = & x \ln (8) (\sin c e \ln (a^{m}) = m \ln (a)) . . . . . . . (1) \end{array}$

We know the formula of differentiation,

$\begin{array}{rcl} \frac{d x^{n}}{d x} & = & n x^{n - 1} \\ \frac{d x}{d x} & = & 1 \\ \frac{d \ln (x)}{d x} & = & \frac{1}{x} \\ \frac{d \ln (f (x))}{d x} & = & \frac{1}{f (x)} \frac{d f (x)}{d x} \end{array}$

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