What is the derivative of tanh(1+e^{4x}) ?

The derivative of tanh(1+e^{4x}) is sech^2(1+e^{4x})*4e^{4x}

What is the first derivative of tanh(1+e^{4x}) ?

The first derivative of tanh(1+e^{4x}) is sech^2(1+e^{4x})*4e^{4x}

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\frac{d}{d x} (tanh (1 + e^{4 x}))

sech^{2} (1 + e^{4 x}) \cdot 4 e^{4 x}

Solution steps

\frac{d}{d x} (tanh (1 + e^{4 x}))

Apply the chain rule:

sech^{2} (1 + e^{4 x}) \frac{d}{d x} (1 + e^{4 x})

= sech^{2} (1 + e^{4 x}) \frac{d}{d x} (1 + e^{4 x})

\frac{d}{d x} (1 + e^{4 x}) = 4 e^{4 x}

= sech^{2} (1 + e^{4 x}) \cdot 4 e^{4 x}

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What is the derivative of tanh(1+e^{4x}) ?
The derivative of tanh(1+e^{4x}) is sech^2(1+e^{4x})*4e^{4x}
What is the first derivative of tanh(1+e^{4x}) ?
The first derivative of tanh(1+e^{4x}) is sech^2(1+e^{4x})*4e^{4x}