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Popular >

derivative of sqrt(x+2)*sin(x)

Solution

\frac{d}{d x} (x + 2 \cdot sin (x))

Solution

\frac{sin ( x )}{2 x + 2} + cos (x) x + 2

Solution steps

\frac{d}{d x} (x + 2 sin (x))

Apply the Product Rule:

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

f = x + 2, g = sin (x)

= \frac{d}{d x} (x + 2) sin (x) + \frac{d}{d x} (sin (x)) x + 2

\frac{d}{d x} (x + 2) = \frac{1}{2 x + 2}

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

= \frac{1}{2 x + 2} sin (x) + cos (x) x + 2

\frac{1}{2 x + 2} sin (x) = \frac{sin ( x )}{2 x + 2}

= \frac{sin ( x )}{2 x + 2} + cos (x) x + 2

Popular Examples

limit as x approaches 0 of 8/(2+e^{1/x)}

x \to 0 lim (\frac{8}{2 + e ^{\frac{1}{x}}})

derivative of (2cos(x)/(1+sin(x)))

\frac{d}{d x} (\frac{2 cos ( x )}{1 + sin ( x )})

limit as x approaches infinity of x^2-x

x \to \infty lim (x^{2} - x)

derivative of f(x)=(12)/(sqrt(x))derivative of

f (x) = \frac{12}{x}

derivative of sec^3(sqrt(x))

\frac{d}{d x} (sec^{3} (x))

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x+2)*sin(x) ?
The derivative of sqrt(x+2)*sin(x) is (sin(x))/(2sqrt(x+2))+cos(x)sqrt(x+2)
What is the first derivative of sqrt(x+2)*sin(x) ?
The first derivative of sqrt(x+2)*sin(x) is (sin(x))/(2sqrt(x+2))+cos(x)sqrt(x+2)