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Popular >

derivative of x^5sin(3x)

Solution

\frac{d}{d x} (x^{5} sin (3 x))

Solution

5 x^{4} sin (3 x) + cos (3 x) \cdot 3 x^{5}

Solution steps

\frac{d}{d x} (x^{5} sin (3 x))

Apply the Product Rule:

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

f = x^{5}, g = sin (3 x)

= \frac{d}{d x} (x^{5}) sin (3 x) + \frac{d}{d x} (sin (3 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 5 x^{4} sin (3 x) + cos (3 x) \cdot 3 x^{5}

Popular Examples

derivative of (x^5-6/x ^{-2})

\frac{d}{d x} ((x^{5} - \frac{6}{x})^{- 2})

integral from 0 to 1 of xe^x

\int_{0}^{1} x e^{x} d x

xyy^'=(y^2-1)^{3/2}

x y y^{^{'}} = (y^{2} - 1)^{\frac{3}{2}}

(\partial)/(\partial y)(xyz+xy^5+yz^5+zx^5)

\frac{\partial}{\partial y} (x yz + x y^{5} + y z^{5} + z x^{5})

integral from 0 to 1 of cos^2(2pix)

\int_{0}^{1} cos^{2} (2 π x) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^5sin(3x) ?
The derivative of x^5sin(3x) is 5x^4sin(3x)+cos(3x)*3x^5
What is the first derivative of x^5sin(3x) ?
The first derivative of x^5sin(3x) is 5x^4sin(3x)+cos(3x)*3x^5