What is the derivative of 4(sin(x+xcos(x))) ?

The derivative of 4(sin(x+xcos(x))) is 4(2cos(x)-xsin(x))

What is the first derivative of 4(sin(x+xcos(x))) ?

The first derivative of 4(sin(x+xcos(x))) is 4(2cos(x)-xsin(x))

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\frac{d}{d x} (4 (sin (x) + x cos (x)))

4 (2 cos (x) - x sin (x))

Solution steps

\frac{d}{d x} (4 (sin (x) + x cos (x)))

Take the constant out:

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

= 4 \frac{d}{d x} (sin (x) + x cos (x))

Apply the Sum/Difference Rule:

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

= 4 (\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)

= 4 (cos (x) + cos (x) - x sin (x))

Simplify

= 4 (2 cos (x) - x sin (x))

\frac{d y}{d x} = 8 x e^{y}

\frac{d}{d x} (3^{x + 1})

\int_{4}^{5} (x^{3} - π x^{2}) d x

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} (8 cos (x) - 6 sin (x))

n = 0 \sum \infty 2^{\frac{1}{n}}

What is the derivative of 4(sin(x+xcos(x))) ?
The derivative of 4(sin(x+xcos(x))) is 4(2cos(x)-xsin(x))
What is the first derivative of 4(sin(x+xcos(x))) ?
The first derivative of 4(sin(x+xcos(x))) is 4(2cos(x)-xsin(x))