- #1

cal.queen92

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## Homework Statement

f(x) = 10(sin(x))^x ----> find f '(1)

## The Attempt at a Solution

I have tried several different approaches, but still get stuck with a wrong answer every time

f(x) = 10(sin(x))^x let f(x) = y so y=10(sin(x))^x then ln y = ln10(sin(x))^x

using log. laws: lny = xln10(sin(x))

then differentiating implicitly using product and chain rule:

1/y*dy/dx = ln10(sin(x)) + 1/10(sinx) * 10(cosx)*x so

1/y*dy/dx = (ln10(sinx)) + (x(cosx)/(sinx))

then multiplying both sides by y to eliminates denominator:

dy/dx = ((10(sinx))^x)*((ln10(sinx))+(x(cosx)/(sinx))

^ this would be the unsimplified derivative ^

Now for f '(1) I would just plug in 1 where ever there is an x right?

I am doing something wrong, can anyone see my mistake? Thank you!