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

The derivative of e^{{g}(x}cos(x)) is e^{{g}(x)}cos(x) derivative of {g}(x)-e^{{g}(x)}sin(x)

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

The first derivative of e^{{g}(x}cos(x)) is e^{{g}(x)}cos(x) derivative of {g}(x)-e^{{g}(x)}sin(x)

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\frac{d}{d x} (e^{g (x)} cos (x))

e^{g (x)} cos (x) \frac{d}{d x} (g (x)) - e^{g (x)} sin (x)

Solution steps

\frac{d}{d x} (e^{g (x)} cos (x))

Apply the Product Rule:

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

f = e^{g (x)}, g = cos (x)

= \frac{d}{d x} (e^{g (x)}) cos (x) + \frac{d}{d x} (cos (x)) e^{g (x)}

\frac{d}{d x} (e^{g (x)}) = e^{g (x)} \frac{d}{d x} (g (x))

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

= e^{g (x)} \frac{d}{d x} (g (x)) cos (x) + (- sin (x)) e^{g (x)}

Simplify

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

f (x) = - 2 x sin (x^{2})

x \to - \infty lim (- 2 x^{3})

x^{2} y^{^{''}} + 17 x y^{^{'}} + 145 y = 0

- 3 cos (x)

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