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))

Take the constant out:

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

= - \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)

y = 3^{1 - x}

x, \frac{1}{x}, x = 3

\int sin (2 x + \frac{π}{2}) d x

f (x) = 3 t - t^{2}

\frac{d}{d x} (\frac{- 6}{( 1 + x ) ^{4}})

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)