### Chapter 3 Test: Question #1

Problem #1: Differentiate y=8^x(sin(x)-cos(x))

Solution:

1) Before we find the derivative of the function, understand the rules that must be applied to find the derivative of this function: Product Rule

2) First, find the two functions that are being multiplied:

**8**

**^x**and

**(sin(x)-cos(x))**

3) Next, find the derivative of both the functions:

d/dx 8^x= d/dx

*e*^((ln 8)x)= e^((ln 8)x) x d/dx(ln a)x= e^((ln 8)x)) x ln 8=

**8^x ln 8**

AND

(sin(x)-cos(x))=(cos(x)-(-sin x))=(cos(x)+sin(x))=

**((sin(x)+cos(x))**

4)Simply plug in the numbers that are required for the product rule:

8^x ln 8(sin(x)-cos(x))+8^x(sin(x)+cos(x)) =

**8^x(sin(x)+cos(x)) + 8^x(sin(x)-cos(x))ln 8**=

**Choice C**

## 1 Comments:

Hi Joseph.

In finding the derivative of 8^x, is it really necessary to go through all that effort? One of our calculus concept sheets is the derivative of an exponential function (not e^x)...

Your derivative is correct, but this is a case where knowing the formula can save some significant time on the test.

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