What is the derivative of 3arcsinh(tan(x)) ?

The derivative of 3arcsinh(tan(x)) is 3sec(x)

What is the first derivative of 3arcsinh(tan(x)) ?

The first derivative of 3arcsinh(tan(x)) is 3sec(x)

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\frac{d}{d x} (3 arcsinh (tan (x)))

3 sec (x)

Solution steps

\frac{d}{d x} (3 arcsinh (tan (x)))

Take the constant out:

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

= 3 \frac{d}{d x} (arcsinh (tan (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

Simplify

3 \cdot \frac{1}{tan ^{2} ( x ) + 1} sec^{2} (x) : 3 sec (x)

= 3 sec (x)

cos (- 5 x)

\int sec^{3} (1) d x

\int 1 - 3 x^{2} d x

\int tan^{2} (6 x) d x

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

What is the derivative of 3arcsinh(tan(x)) ?
The derivative of 3arcsinh(tan(x)) is 3sec(x)
What is the first derivative of 3arcsinh(tan(x)) ?
The first derivative of 3arcsinh(tan(x)) is 3sec(x)