What is the derivative of y=xe^{sin(x)} ?

The derivative of y=xe^{sin(x)} is e^{sin(x)}+e^{sin(x)}xcos(x)

What is the first derivative of y=xe^{sin(x)} ?

The first derivative of y=xe^{sin(x)} is e^{sin(x)}+e^{sin(x)}xcos(x)

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derivative of

y = x e^{s i n (x)}

e^{s i n (x)} + e^{s i n (x)} x cos (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{s i n (x)}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{s i n (x)} + e^{s i n (x)} cos (x) x

Simplify

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

What is the derivative of y=xe^{sin(x)} ?
The derivative of y=xe^{sin(x)} is e^{sin(x)}+e^{sin(x)}xcos(x)
What is the first derivative of y=xe^{sin(x)} ?
The first derivative of y=xe^{sin(x)} is e^{sin(x)}+e^{sin(x)}xcos(x)