What is the derivative of tanh(sqrt(x)) ?

The derivative of tanh(sqrt(x)) is (sech^2(sqrt(x)))/(2sqrt(x))

What is the first derivative of tanh(sqrt(x)) ?

The first derivative of tanh(sqrt(x)) is (sech^2(sqrt(x)))/(2sqrt(x))

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\frac{d}{d x} (tanh (x))

\frac{sech ^{2} ( x )}{2 x}

Solution steps

\frac{d}{d x} (tanh (x))

Apply the chain rule:

sech^{2} (x) \frac{d}{d x} (x)

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

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

= sech^{2} (x) \frac{1}{2 x}

Simplify

sech^{2} (x) \frac{1}{2 x} : \frac{sech ^{2} ( x )}{2 x}

= \frac{sech ^{2} ( x )}{2 x}

What is the derivative of tanh(sqrt(x)) ?
The derivative of tanh(sqrt(x)) is (sech^2(sqrt(x)))/(2sqrt(x))
What is the first derivative of tanh(sqrt(x)) ?
The first derivative of tanh(sqrt(x)) is (sech^2(sqrt(x)))/(2sqrt(x))