What is the derivative of arctan(x^2y) ?

The derivative of arctan(x^2y) is (2xy+x^2\frac{dy)/(dx)}{x^4y^2+1}

What is the first derivative of arctan(x^2y) ?

The first derivative of arctan(x^2y) is (2xy+x^2\frac{dy)/(dx)}{x^4y^2+1}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 11 x ln (x) d x

f (x) = - \frac{2}{x ^{3}}

\int (1 - x^{2})^{- 0.5} d x

- \frac{z}{e ^{z + 1} ( z - 1 ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x - x^{- 1} + x^{- 3})

What is the derivative of arctan(x^2y) ?
The derivative of arctan(x^2y) is (2xy+x^2\frac{dy)/(dx)}{x^4y^2+1}
What is the first derivative of arctan(x^2y) ?
The first derivative of arctan(x^2y) is (2xy+x^2\frac{dy)/(dx)}{x^4y^2+1}