Find d y d x if y = e x s i n x Options: A . &nbspexcosx B . &nbspex+cosx C . &nbspex(cosx+sinx) D . &nbspnone of these

Answer: Option C : C y = e x s i n x . So d y d x = d d x ( e x s i n x ) = e x d d x ( s i n x ) + s i n x d d x ( e x ) = e x c o s x + e x s i n x = e x ( c o s x + s i n x ) .

Find dydx if y=ex sinx

Question

Find

\frac{d y}{d x}

y = e^{x} s i n x

Options:

A . excosx

B . ex+cosx

C . ex(cosx+sinx)

D . none of these

Answer: Option C
:
C

y = e^{x} s i n x

.
So

\frac{d y}{d x} = \frac{d}{d x} (e^{x} s i n x) = e^{x} \frac{d}{d x} (s i n x) + s i n x \frac{d}{d x} (e^{x})

e^{x} c o s x + e^{x} s i n x = e^{x} (c o s x + s i n x)

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