What is the derivative of y with respect to x for y = 17^x?

2 Answers
Nov 26, 2015

The derivative is f'(x)=dy/dx=d17^x/dx=17^x*ln17

Explanation:

The general rule of differentiating exponential functions is that:

(a^x)'=(a^x)*lna

Dec 30, 2015

y'=17^x*ln17

Explanation:

The first step is to rewrite 17^x as something differentiable.

y=17^x=e^(ln17^x)=e^(xln17)

e^(xln17) is differentiable since we can use the chain rule:

d/dx(e^u)=e^u*u'

Apply this to e^(xln17):

y'=d/dx(e^(xln17))=e^(xln17)*d/dx(xln17)

Two things to consider here:

color(white)(sss) e^(xln17) is still equal to 17^x, we can rewrite it as such now that
color(white)(sss) we've differentiated.

color(white)(sss) d/dx(xln17)=ln17
color(white)(sss) Remember, ln17 is just a constant. Don't be fooled by it.

Thus,

y'=17^x*ln17