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Popular >

derivative of 3(sin(x+xcos(x)))

Solution

\frac{d}{d x} (3 (sin (x) + x cos (x)))

Solution

3 (2 cos (x) - x sin (x))

Solution steps

\frac{d}{d x} (3 (sin (x) + x cos (x)))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (x) + x cos (x))

Apply the Sum/Difference Rule:

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

= 3 (\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)

= 3 (cos (x) + cos (x) - x sin (x))

Simplify

= 3 (2 cos (x) - x sin (x))

Popular Examples

sum from n=1 to infinity of 2^{1/n}

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

(\partial)/(\partial x)(3x^2+2xy)

\frac{\partial}{\partial x} (3 x^{2} + 2 x y)

integral of 1/(4^x)

\int \frac{1}{4 ^{x}} d x

integral of xe^{-6x^2}

\int x e^{- 6 x^{2}} d x

limit as x approaches-2 of 4x^2-3x+5

x \to - 2 lim (4 x^{2} - 3 x + 5)

Frequently Asked Questions (FAQ)

What is the derivative of 3(sin(x+xcos(x))) ?
The derivative of 3(sin(x+xcos(x))) is 3(2cos(x)-xsin(x))
What is the first derivative of 3(sin(x+xcos(x))) ?
The first derivative of 3(sin(x+xcos(x))) is 3(2cos(x)-xsin(x))