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Popular >

derivative of 5arctan(x^2)

Solution

\frac{d}{d x} (5 arctan (x^{2}))

Solution

\frac{10 x}{x ^{4} + 1}

Solution steps

\frac{d}{d x} (5 arctan (x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{( x ^{2} ) ^{2} + 1} \frac{d}{d x} (x^{2})

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

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

= 5 \cdot \frac{1}{( x ^{2} ) ^{2} + 1} \cdot 2 x

Simplify

5 \cdot \frac{1}{( x ^{2} ) ^{2} + 1} \cdot 2 x : \frac{10 x}{x ^{4} + 1}

= \frac{10 x}{x ^{4} + 1}

Popular Examples

derivative of (1-5x/x)

\frac{d}{d x} (\frac{1 - 5 x}{x})

derivative of xy^2-x^2y+xy

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

derivative of 2x^2+1/(x^2)derivative of

2 x^{2} + \frac{1}{x ^{2}}

integral of (x^3)/((x^2-256)^{3/2)}

\int \frac{x ^{3}}{( x ^{2} - 256 ) ^{\frac{3}{2}}} d x

slope of (0,-10),(6,10)slope

(0, - 10), (6, 10)

Frequently Asked Questions (FAQ)

What is the derivative of 5arctan(x^2) ?
The derivative of 5arctan(x^2) is (10x)/(x^4+1)
What is the first derivative of 5arctan(x^2) ?
The first derivative of 5arctan(x^2) is (10x)/(x^4+1)