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Popular >

derivative of 3arctan(2x)

Solution

\frac{d}{d x} (3 arctan (2 x))

Solution

\frac{6}{4 x ^{2} + 1}

Solution steps

\frac{d}{d x} (3 arctan (2 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (arctan (2 x))

Apply the chain rule:

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

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

\frac{d}{d x} (2 x) = 2

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

Simplify

3 \cdot \frac{1}{( 2 x ) ^{2} + 1} \cdot 2 : \frac{6}{4 x ^{2} + 1}

= \frac{6}{4 x ^{2} + 1}

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(dy)/(dx)=y(x^2+2)

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derivative of 8e^{-7x}derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of 3arctan(2x) ?
The derivative of 3arctan(2x) is 6/(4x^2+1)
What is the first derivative of 3arctan(2x) ?
The first derivative of 3arctan(2x) is 6/(4x^2+1)