What is the derivative of arccot(5x^2) ?

The derivative of arccot(5x^2) is -(10x)/(25x^4+1)

What is the first derivative of arccot(5x^2) ?

The first derivative of arccot(5x^2) is -(10x)/(25x^4+1)

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

- \frac{10 x}{25 x ^{4} + 1}

Solution steps

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

Apply the chain rule:

- \frac{1}{( 5 x ^{2} ) ^{2} + 1} \frac{d}{d x} (5 x^{2})

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

\frac{d}{d x} (5 x^{2}) = 10 x

= - \frac{1}{( 5 x ^{2} ) ^{2} + 1} \cdot 10 x

Simplify

- \frac{1}{( 5 x ^{2} ) ^{2} + 1} \cdot 10 x : - \frac{10 x}{25 x ^{4} + 1}

= - \frac{10 x}{25 x ^{4} + 1}

\frac{\partial}{\partial x} (e^{i x})

y^{^{'}} + y = t

\frac{d}{d x} (\frac{x}{x + 3})

\int \frac{1}{x ^{2} 9 + x ^{2}} d x

(x + 2) sin (y) d x + x cos (y) d y = 0

What is the derivative of arccot(5x^2) ?
The derivative of arccot(5x^2) is -(10x)/(25x^4+1)
What is the first derivative of arccot(5x^2) ?
The first derivative of arccot(5x^2) is -(10x)/(25x^4+1)