What is the derivative of cosh(xcos(x^2)) ?

The derivative of cosh(xcos(x^2)) is sinh(x)cos(x^2)-2xsin(x^2)cosh(x)

What is the first derivative of cosh(xcos(x^2)) ?

The first derivative of cosh(xcos(x^2)) is sinh(x)cos(x^2)-2xsin(x^2)cosh(x)

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\frac{d}{d x} (cosh (x) cos (x^{2}))

sinh (x) cos (x^{2}) - 2 x sin (x^{2}) cosh (x)

Solution steps

\frac{d}{d x} (cosh (x) cos (x^{2}))

Apply the Product Rule:

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

f = cosh (x), g = cos (x^{2})

= \frac{d}{d x} (cosh (x)) cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) cosh (x)

\frac{d}{d x} (cosh (x)) = sinh (x)

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

= sinh (x) cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) cosh (x)

Simplify

= sinh (x) cos (x^{2}) - 2 x sin (x^{2}) cosh (x)

What is the derivative of cosh(xcos(x^2)) ?
The derivative of cosh(xcos(x^2)) is sinh(x)cos(x^2)-2xsin(x^2)cosh(x)
What is the first derivative of cosh(xcos(x^2)) ?
The first derivative of cosh(xcos(x^2)) is sinh(x)cos(x^2)-2xsin(x^2)cosh(x)