What is the derivative of 4^{cosh(x)} ?

The derivative of 4^{cosh(x)} is ln(2)*2^{2cosh(x)+1}sinh(x)

What is the first derivative of 4^{cosh(x)} ?

The first derivative of 4^{cosh(x)} is ln(2)*2^{2cosh(x)+1}sinh(x)

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derivative of

4^{c o s h (x)}

ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)

Solution steps

\frac{d}{d x} (4^{c o s h (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

4^{c o s h (x)} = e^{c o s h (x) l n (4)}

= \frac{d}{d x} (e^{c o s h (x) l n (4)})

Apply the chain rule:

e^{c o s h (x) l n (4)} \frac{d}{d x} (cosh (x) ln (4))

= e^{c o s h (x) l n (4)} \frac{d}{d x} (cosh (x) ln (4))

\frac{d}{d x} (cosh (x) ln (4)) = 2 ln (2) sinh (x)

= e^{c o s h (x) l n (4)} \cdot 2 ln (2) sinh (x)

Simplify

e^{c o s h (x) l n (4)} \cdot 2 ln (2) sinh (x) : ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)

= ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)

What is the derivative of 4^{cosh(x)} ?
The derivative of 4^{cosh(x)} is ln(2)*2^{2cosh(x)+1}sinh(x)
What is the first derivative of 4^{cosh(x)} ?
The first derivative of 4^{cosh(x)} is ln(2)*2^{2cosh(x)+1}sinh(x)