Question

derivative of e^(9x)=sin(x+7y)

Answer 1

\[9e^{9x}=\cos(x+7y)\times \left(1+7y'\right)\] solve for \(y'\)

Answer 2

can you help me through this part im not sure

Answer 3

the hard part is knowing how to use the chain rule properly to get started with what i wrote above
is that part ok?

Answer 4

the chain rule is first times derivative of the second plus second times derivative of the first right?

Answer 5

no, that is the product rule

Answer 6

oh ok which is the chain rule again?

Answer 7

\[\left(f(g)\right)'=f'(g)g'\]

Answer 8

for example
\[\frac{d}{dx}e^{9x}=e^{9x}\times \frac{d}{dx}9x=9e^{9x}\]

Answer 9

and
\[\frac{d}{dx}\sin(x+7y)=\cos(x+7y)\times \frac{d}{dx}[x+7y]\]
\[=\cos(x+7y)\times (1+7y')\]

Answer 10

9e^(9x)(9x^(-1/2))=cos(7x+14y)