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Popular >

derivative of f(x)=arctan(x^2)

Solution

derivative of

f (x) = arctan (x^{2})

Solution

\frac{2 x}{x ^{4} + 1}

Solution steps

\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

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

Simplify

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

= \frac{2 x}{x ^{4} + 1}

Popular Examples

tangent of (ln(x^2-10x-10)),\at x=11 tangent of

(ln (x^{2} - 10 x - 10)), at x = 11

(x^2+1)((dy)/(dx))+3x(y-1)=0,y(0)=8

(x^{2} + 1) (\frac{d y}{d x}) + 3 x (y - 1) = 0, y (0) = 8

limit as x approaches-3 of xsqrt(x+3)

x \to - 3 lim (x x + 3)

(\partial)/(\partial z)(6ze^{xyz})

\frac{\partial}{\partial z} (6 z e^{x yz})

integral of (sqrt(5+2tan(x)))/(cos^2(x))

\int \frac{5 + 2 tan ( x )}{cos ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

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