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Popular >

derivative of x^3arctan(5x)

Solution

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

Solution

3 x^{2} arctan (5 x) + \frac{5 x ^{3}}{25 x ^{2} + 1}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= 3 x^{2} arctan (5 x) + \frac{5}{25 x ^{2} + 1} x^{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 3 x^{2} arctan (5 x) + \frac{5 x ^{3}}{25 x ^{2} + 1}

Popular Examples

integral of (9(1-tan^2(x)))/(sec^2(x))

\int \frac{9 ( 1 - tan ^{2} ( x ) )}{sec ^{2} ( x )} d x

derivative of csc(x+cot(x))

\frac{d}{d x} (csc (x) + cot (x))

derivative of (ln(x))/(5x^3)derivative of

\frac{ln ( x )}{5 x ^{3}}

(4x^3y^2-6x^2y-2x-3)dx+(2x^4y-2x^3)dy=0

(4 x^{3} y^{2} - 6 x^{2} y - 2 x - 3) d x + (2 x^{4} y - 2 x^{3}) d y = 0

laplacetransform e^{-t}sin(3t)laplace transform

e^{- t} sin (3 t)

Frequently Asked Questions (FAQ)

What is the derivative of x^3arctan(5x) ?
The derivative of x^3arctan(5x) is 3x^2arctan(5x)+(5x^3)/(25x^2+1)
What is the first derivative of x^3arctan(5x) ?
The first derivative of x^3arctan(5x) is 3x^2arctan(5x)+(5x^3)/(25x^2+1)