Question

if y= 4^x *ln(x) find dy/dx

Answer 1

this is a bit tricky... but doable with implicit differentiation..

Answer 2

4^xln4lnx + 4^x/x

Answer 3

Using the chain rule we get:
\[dy/dx = 4^x*(1/x)+ln(x)*(4^x)'\]

Answer 4

now we just need to find what the derivative of\[4^x\]is

Answer 5

\[f=4^x\]\[f'-?\]\[ln(f)=x*ln(4)\]

Answer 6

\[\frac{1}{f}\frac{df}{dx}=ln(4)\]

Answer 7

\[\frac{df}{dx}=ln(4) * f\]
\[\frac{df}{dx}=ln(4)*4^x=4^x*ln(4)\]

Answer 8

Plugging that into the original equation gives us:
\[\frac{dy}{dx} = \frac{4^x}{x}+ln(x)*(4^x)'\]\[\frac{dy}{dx}=\frac{4^x}{x}+ln(x)*(4^x*ln(4))\]

Answer 9

wow @kaylalynn you're a noob I had the answer for you yet u medal him

Answer 10

^you didn't explain. I could have used a calculator and gotten the answer in seconds myself as well.

Answer 11

sorry @TanteAnna I didn't see your response. However he did show the work.

Answer 12

Well I didn't use a calculator this question is so simple you don't need work this is 2nd grade material, yo.