What is the derivative of e^{cosh(x}cos^2(x)) ?

The derivative of e^{cosh(x}cos^2(x)) is e^{cosh(x)}cos^2(x)sinh(x)-e^{cosh(x)}sin(2x)

What is the first derivative of e^{cosh(x}cos^2(x)) ?

The first derivative of e^{cosh(x}cos^2(x)) is e^{cosh(x)}cos^2(x)sinh(x)-e^{cosh(x)}sin(2x)

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\frac{d}{d x} (e^{c o s h (x)} cos^{2} (x))

e^{c o s h (x)} cos^{2} (x) sinh (x) - e^{c o s h (x)} sin (2 x)

Solution steps

\frac{d}{d x} (e^{c o s h (x)} cos^{2} (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{c o s h (x)}, g = cos^{2} (x)

= \frac{d}{d x} (e^{c o s h (x)}) cos^{2} (x) + \frac{d}{d x} (cos^{2} (x)) e^{c o s h (x)}

\frac{d}{d x} (e^{c o s h (x)}) = e^{c o s h (x)} sinh (x)

\frac{d}{d x} (cos^{2} (x)) = - sin (2 x)

= e^{c o s h (x)} sinh (x) cos^{2} (x) + (- sin (2 x)) e^{c o s h (x)}

Simplify

= e^{c o s h (x)} cos^{2} (x) sinh (x) - e^{c o s h (x)} sin (2 x)

What is the derivative of e^{cosh(x}cos^2(x)) ?
The derivative of e^{cosh(x}cos^2(x)) is e^{cosh(x)}cos^2(x)sinh(x)-e^{cosh(x)}sin(2x)
What is the first derivative of e^{cosh(x}cos^2(x)) ?
The first derivative of e^{cosh(x}cos^2(x)) is e^{cosh(x)}cos^2(x)sinh(x)-e^{cosh(x)}sin(2x)