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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int_{0}^{a} x sin^{2} (\frac{π x}{a}) d x

\int_{1}^{9} 9 x^{2} d x

y = \frac{88 t}{99 t - 88}

\frac{d}{d x} (x - y^{2})

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

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