What is the derivative of arctan(4t) ?

The derivative of arctan(4t) is 4/(16t^2+1)

What is the first derivative of arctan(4t) ?

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

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derivative of

arctan (4 t)

\frac{4}{16 t ^{2} + 1}

Solution steps

\frac{d}{d t} (arctan (4 t))

Apply the chain rule:

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

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

\frac{d}{d t} (4 t) = 4

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

Simplify

\frac{1}{( 4 t ) ^{2} + 1} \cdot 4 : \frac{4}{16 t ^{2} + 1}

= \frac{4}{16 t ^{2} + 1}

\int \frac{x ^{2}}{3 - x ^{3}} d x

1500 x + 3000 (5 x + 3)^{- 1} - 1000

\frac{e ^{- 4 s}}{s}

\int_{0}^{\frac{5}{4}} \frac{1}{25 + 16 x ^{2}} d x

\frac{d}{d x} (y ln (x))

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