Question

find, from first principles, the derivative of
y= (sinx)(e^x)

Answer 1

\[\frac{ dy }{ dx }= \lim_{h \rightarrow 0} \frac{e ^{x+h} \sin(x+h) - e^{x} sinx}{h}\]

Answer 2

Maybe try an angle sum identity for sin(x+h), and for e^{x+h}, you add the exponents when multiplying powers of the same base. See if you can use that to factor things out.

Answer 3

i did the question till,

\[\lim_{h \rightarrow 0}\frac{e^x e^h sinx \cosh + e^x e^h cosxsinh -e^xsinx}{h}\]

but i can't eliminate the terms

Answer 4

add some increment to both sides.