What is the derivative of a(sin(x+xcos(x))) ?

The derivative of a(sin(x+xcos(x))) is a(2cos(x)-xsin(x))

What is the first derivative of a(sin(x+xcos(x))) ?

The first derivative of a(sin(x+xcos(x))) is a(2cos(x)-xsin(x))

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\frac{d}{d x} (a (sin (x) + x cos (x)))

a (2 cos (x) - x sin (x))

Solution steps

\frac{d}{d x} (a (sin (x) + x cos (x)))

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= a (cos (x) + cos (x) - x sin (x))

Simplify

= a (2 cos (x) - x sin (x))

ln (x), e

\int 3 cos^{5} (3 x) d x

(y - x) d x + (x + y) d y = 0

\int \frac{e ^{2 x}}{e ^{x} + 4} d x

\frac{d}{d x} (ln^{3} (5 x))

What is the derivative of a(sin(x+xcos(x))) ?
The derivative of a(sin(x+xcos(x))) is a(2cos(x)-xsin(x))
What is the first derivative of a(sin(x+xcos(x))) ?
The first derivative of a(sin(x+xcos(x))) is a(2cos(x)-xsin(x))