What is (\partial)/(\partial x)(-e^{cos(x)}sin(x)) ?

The answer to (\partial)/(\partial x)(-e^{cos(x)}sin(x)) is e^{cos(x)}sin^2(x)-e^{cos(x)}cos(x)

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(\partial)/(\partial x)(-e^{cos(x)}sin(x))

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

\frac{\partial}{\partial 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)

\frac{d}{d x} (100 x^{0.25} y^{0.75})

\int_{- 1}^{1} (e^{x} - (x^{2} - 2)) d x

\frac{d y}{d x} = \frac{1}{x ln ( 2 )}

3 e^{2 x^{2}}

\int \frac{9000 - 3000 x}{( x ^{2} - 6 x + 10 ) ^{2}} d x

What is (\partial)/(\partial x)(-e^{cos(x)}sin(x)) ?
The answer to (\partial)/(\partial x)(-e^{cos(x)}sin(x)) is e^{cos(x)}sin^2(x)-e^{cos(x)}cos(x)