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Popular Calculus >

derivative of x^3sin(5x)

Solution

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

Solution

3 x^{2} sin (5 x) + cos (5 x) \cdot 5 x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 3 x^{2} sin (5 x) + cos (5 x) \cdot 5 x^{3}

Graph

Popular Examples

derivative of x^4-4x^3+4x^2

\frac{d}{d x} (x^{4} - 4 x^{3} + 4 x^{2})

integral of (1+x+x^2)ln(x)

\int (1 + x + x^{2}) ln (x) d x

derivative of y=-csc(x)-sin(x)

d er i v a t i v e y = - csc (x) - sin (x)

y^{''}-4y^'-5y=-3e^4t,y(0)=0,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} - 5 y = - 3 e^{4} t, y (0) = 0, y^{^{'}} (0) = 0

integral from 1 to x of (1/(t^3+1))

\int_{1}^{x} (\frac{1}{t ^{3} + 1}) d t

Frequently Asked Questions (FAQ)

What is the derivative of x^3sin(5x) ?
The derivative of x^3sin(5x) is 3x^2sin(5x)+cos(5x)*5x^3
What is the first derivative of x^3sin(5x) ?
The first derivative of x^3sin(5x) is 3x^2sin(5x)+cos(5x)*5x^3