What is the derivative of e^{arctan(4t^2)} ?

The derivative of e^{arctan(4t^2)} is (8e^{arctan(4t^2)}t)/(16t^4+1)

What is the first derivative of e^{arctan(4t^2)} ?

The first derivative of e^{arctan(4t^2)} is (8e^{arctan(4t^2)}t)/(16t^4+1)

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derivative of

e^{a r c t a n (4 t^{2})}

\frac{8 e ^{a r c t a n (4 t^{2})} t}{16 t ^{4} + 1}

Solution steps

\frac{d}{d t} (e^{a r c t a n (4 t^{2})})

Apply the chain rule:

e^{a r c t a n (4 t^{2})} \frac{d}{d t} (arctan (4 t^{2}))

= e^{a r c t a n (4 t^{2})} \frac{d}{d t} (arctan (4 t^{2}))

\frac{d}{d t} (arctan (4 t^{2})) = \frac{8 t}{16 t ^{4} + 1}

= e^{a r c t a n (4 t^{2})} \frac{8 t}{16 t ^{4} + 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 e ^{a r c t a n (4 t^{2})} t}{16 t ^{4} + 1}

\frac{d}{d x} (- \frac{11}{x ^{5}})

\int x e^{6 x} d x

\int x \cdot sin (5 x) d x

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

\int_{- π}^{π} sin^{2} (x co) s^{3} x d x

What is the derivative of e^{arctan(4t^2)} ?
The derivative of e^{arctan(4t^2)} is (8e^{arctan(4t^2)}t)/(16t^4+1)
What is the first derivative of e^{arctan(4t^2)} ?
The first derivative of e^{arctan(4t^2)} is (8e^{arctan(4t^2)}t)/(16t^4+1)