What is the derivative of sin(xe^{cos(x)}) ?

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

What is the first derivative of sin(xe^{cos(x)}) ?

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

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\frac{d}{d x} (sin (x) e^{c o s (x)})

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

Solution steps

\frac{d}{d x} (sin (x) e^{c o s (x)})

Apply the Product Rule:

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

f = sin (x), g = e^{c o s (x)}

= \frac{d}{d x} (sin (x)) e^{c o s (x)} + \frac{d}{d x} (e^{c o s (x)}) sin (x)

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

\frac{d}{d x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

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

Simplify

cos (x) e^{c o s (x)} + (- e^{c o s (x)} sin (x)) sin (x) : e^{c o s (x)} cos (x) - e^{c o s (x)} sin^{2} (x)

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

3 t^{4}

\frac{d}{d x} ((2 x - 5) (3 - 2 x^{2}))

y = \frac{1}{x ^{2}}, (2, \frac{1}{4})

(t + 1)^{^{'}}

\int \frac{8}{x ( x + 2 )} d x

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