Question

find dy/dx if y=sin^2 x +2^(sinx)

Answer 1

first part is ok right? you get \(2\sin(x)\cos(x)\) for the derivative of \(\sin^2(x)\) by the chain rule

Answer 2

yes

Answer 3

as for \(2^{\sin(x)}\) this is also a chain rule problem, so long as you remember that the derivative of \(b^x\) is \(b^x\ln(b)\)

Answer 4

in this case you get
\[2^{\sin(x)}\ln(2)\cos(x)\]

Answer 5

so thatd be 2^sinx ln (2)?

Answer 6

you gotta multiply by the derivative of sine, as per the chain rule

Answer 7

ok so we get 2sinxcosx + 2^sinx ln2 cos x

Answer 8

yes
you can factor out the cosine if you like
or not

Answer 9

do you factor out sinxcosx?

Answer 10

your common factor is only cosine
the sine in the second part is in the exponent

Answer 11

oh ok

Answer 12

ok i just re-worked it out...now i see what you were talking about

Answer 13

thank you very much for your help :)