What is the derivative of arctan(x^5) ?

The derivative of arctan(x^5) is (5x^4)/(x^{10)+1}

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

The first derivative of arctan(x^5) is (5x^4)/(x^{10)+1}

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

\frac{5 x ^{4}}{x ^{10} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

Simplify

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

= \frac{5 x ^{4}}{x ^{10} + 1}

\frac{\partial}{\partial y} (y^{2 x})

x \to - 2 lim (4 x^{3} + 4 x - 2)

8 - x^{2}, x^{2}, (- 3, 3)

\frac{1}{x + 1}

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