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Popular >

derivative of 6arcsinh(tan(x))

Solution

\frac{d}{d x} (6 arcsinh (tan (x)))

Solution

6 sec (x)

Solution steps

\frac{d}{d x} (6 arcsinh (tan (x)))

Take the constant out:

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

= 6 \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)

= 6 \cdot \frac{1}{( tan ( x ) ) ^{2} + 1} sec^{2} (x)

Simplify

6 \cdot \frac{1}{tan ^{2} ( x ) + 1} sec^{2} (x) : 6 sec (x)

= 6 sec (x)

Popular Examples

(\partial)/(\partial x)(ln(6x^2-4y^2))

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

limit as x approaches 7 of (9x)/(x-7)

x \to 7 lim (\frac{9 x}{x - 7})

(dy)/(dx)=e^{-x}-y

\frac{d y}{d x} = e^{- x} - y

derivative of y=x^{17/18}derivative of

y = x^{\frac{17}{18}}

(\partial)/(\partial y)(y*ln(x))

\frac{\partial}{\partial y} (y \cdot ln (x))

Frequently Asked Questions (FAQ)

What is the derivative of 6arcsinh(tan(x)) ?
The derivative of 6arcsinh(tan(x)) is 6sec(x)
What is the first derivative of 6arcsinh(tan(x)) ?
The first derivative of 6arcsinh(tan(x)) is 6sec(x)