What is the derivative of y=arctan(ln(2)x^5) ?

The derivative of y=arctan(ln(2)x^5) is (5ln(2)x^4)/(ln^2(2)x^{10)+1}

What is the first derivative of y=arctan(ln(2)x^5) ?

The first derivative of y=arctan(ln(2)x^5) is (5ln(2)x^4)/(ln^2(2)x^{10)+1}

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derivative of

y = arctan (ln (2) x^{5})

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (2) x^{5}) = 5 ln (2) x^{4}

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

Simplify

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

= \frac{5 ln ( 2 ) x ^{4}}{ln ^{2} ( 2 ) x ^{10} + 1}

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

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{5})

y = x^{2} - x + 9

\frac{d y}{( 5 - 3 y ) ^{2}} = \frac{d x}{2 ( 4 - x )}

e^{- 0.75 t} cos (4 t)

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