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Popular >

derivative of xe^{sin(x})

Solution

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

Solution

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)

Popular Examples

sum from n=1 to infinity}(3^{n+2 of)/(5^n)

n = 1 \sum \infty \frac{3 ^{n + 2}}{5 ^{n}}

derivative of (r^5-4r)e^r derivative of

(r^{5} - 4 r) e^{r}

(dy)/(dx)=(sqrt(y^2-9)),y(1)=4

\frac{d y}{d x} = (y^{2} - 9), y (1) = 4

integral of e^xcos(x/2)

\int e^{x} cos (\frac{x}{2}) d x

integral of 2/(x^{-1)+1}

\int \frac{2}{x ^{- 1} + 1} d x

Frequently Asked Questions (FAQ)

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