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

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

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

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

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\frac{d}{d x} (e^{s i n (x)} cos (x))

e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

Solution steps

\frac{d}{d x} (e^{s i n (x)} cos (x))

Apply the Product Rule:

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

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

= \frac{d}{d x} (e^{s i n (x)}) cos (x) + \frac{d}{d x} (cos (x)) e^{s i n (x)}

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

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

= e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)}

Simplify

e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)} : e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

= e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

\int \frac{1}{tanh ( 3 x )} d x

3 y^{^{''}} + 75 y = 81 sin (4 t)

y = x^{3}, (2, 8)

y^{^{''}} + 8 y^{^{'}} + 16 y = 2 e^{- 4 t}

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