What is the derivative of y=arctan(4t) ?

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

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

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

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derivative of

y = 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}

x \to 2 - lim (2 - x^{2})

x^{2} \frac{d y}{d x} = 2 y

(\frac{g ( t )}{f ( t )})^{'}

ln (1 - x^{2})

\frac{d}{d x} (a e^{- a x})

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