What is the derivative of y=arctan(ln(2)x^4) ?

The derivative of y=arctan(ln(2)x^4) is (4ln(2)x^3)/(ln^2(2)x^8+1)

What is the first derivative of y=arctan(ln(2)x^4) ?

The first derivative of y=arctan(ln(2)x^4) is (4ln(2)x^3)/(ln^2(2)x^8+1)

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derivative of

y = arctan (ln (2) x^{4})

\frac{4 ln ( 2 ) x ^{3}}{ln ^{2} ( 2 ) x ^{8} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (2) x^{4}) = 4 ln (2) x^{3}

= \frac{1}{( ln ( 2 ) x ^{4} ) ^{2} + 1} \cdot 4 ln (2) x^{3}

Simplify

\frac{1}{( ln ( 2 ) x ^{4} ) ^{2} + 1} \cdot 4 ln (2) x^{3} : \frac{4 ln ( 2 ) x ^{3}}{ln ^{2} ( 2 ) x ^{8} + 1}

= \frac{4 ln ( 2 ) x ^{3}}{ln ^{2} ( 2 ) x ^{8} + 1}

(- 3, 4), (4, 1)

\int_{- 2}^{1} \frac{1}{2} x^{2} + x + 1 d x

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

\frac{d}{d x} (x e^{x^{2} - y})

(1 + t) (2 t^{2} - 7)

What is the derivative of y=arctan(ln(2)x^4) ?
The derivative of y=arctan(ln(2)x^4) is (4ln(2)x^3)/(ln^2(2)x^8+1)
What is the first derivative of y=arctan(ln(2)x^4) ?
The first derivative of y=arctan(ln(2)x^4) is (4ln(2)x^3)/(ln^2(2)x^8+1)