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Popular >

derivative of y=e^{arctan(3t^2)}

Solution

derivative of

y = e^{a r c t a n (3 t^{2})}

Solution

\frac{6 e ^{a r c t a n (3 t^{2})} t}{9 t ^{4} + 1}

Solution steps

\frac{d}{d t} (e^{a r c t a n (3 t^{2})})

Apply the chain rule:

e^{a r c t a n (3 t^{2})} \frac{d}{d t} (arctan (3 t^{2}))

= e^{a r c t a n (3 t^{2})} \frac{d}{d t} (arctan (3 t^{2}))

\frac{d}{d t} (arctan (3 t^{2})) = \frac{6 t}{9 t ^{4} + 1}

= e^{a r c t a n (3 t^{2})} \frac{6 t}{9 t ^{4} + 1}

Multiply fractions:

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

= \frac{6 e ^{a r c t a n (3 t^{2})} t}{9 t ^{4} + 1}

Popular Examples

derivative of 5xsin(pix)

\frac{d}{d x} (5 x sin (π x))

derivative of (3000/(x+3600x^{-1)})

\frac{d}{d x} (\frac{3000}{x + 3600 x ^{- 1}})

inverse oflaplace 9/(s(s^2+2s+9))inverse laplace

\frac{9}{s ( s ^{2} + 2 s + 9 )}

tangent of f(x)= 1/(x+1),(-2,-1)tangent of

f (x) = \frac{1}{x + 1}, (- 2, - 1)

derivative of (6x^2+7x^4)

\frac{d}{d x} ((6 x^{2} + 7 x)^{4})

Frequently Asked Questions (FAQ)

What is the derivative of y=e^{arctan(3t^2)} ?
The derivative of y=e^{arctan(3t^2)} is (6e^{arctan(3t^2)}t)/(9t^4+1)
What is the first derivative of y=e^{arctan(3t^2)} ?
The first derivative of y=e^{arctan(3t^2)} is (6e^{arctan(3t^2)}t)/(9t^4+1)