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Popular >

derivative of x^8sin(x)

Solution

\frac{d}{d x} (x^{8} sin (x))

Solution

8 x^{7} sin (x) + cos (x) x^{8}

Solution steps

\frac{d}{d x} (x^{8} sin (x))

Apply the Product Rule:

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

f = x^{8}, g = sin (x)

= \frac{d}{d x} (x^{8}) sin (x) + \frac{d}{d x} (sin (x)) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (sin (x)) = cos (x)

= 8 x^{7} sin (x) + cos (x) x^{8}

Popular Examples

(\partial}{\partial x}(\frac{x^4)/y)

\frac{\partial}{\partial x} (\frac{x ^{4}}{y})

(\partial)/(\partial y)(6+xln(xy-5))

\frac{\partial}{\partial y} (6 + x ln (x y - 5))

integral of 3sin^3(x)cos^7(x)

\int 3 sin^{3} (x) cos^{7} (x) d x

area x=16-y^2,x=y^2-16 area

x = 16 - y^{2}, x = y^{2} - 16

sum from n=6 to infinity of (3n)/(12n)

n = 6 \sum \infty \frac{3 n}{12 n}

Frequently Asked Questions (FAQ)

What is the derivative of x^8sin(x) ?
The derivative of x^8sin(x) is 8x^7sin(x)+cos(x)x^8
What is the first derivative of x^8sin(x) ?
The first derivative of x^8sin(x) is 8x^7sin(x)+cos(x)x^8