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Popular >

derivative of sqrt(x)(x^5+2)

Solution

derivative of

x (x^{5} + 2)

Solution

\frac{11 x ^{5} + 2}{2 x}

Solution steps

\frac{d}{d x} (x (x^{5} + 2))

Apply the Product Rule:

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

f = x, g = x^{5} + 2

= \frac{d}{d x} (x) (x^{5} + 2) + \frac{d}{d x} (x^{5} + 2) x

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

\frac{d}{d x} (x^{5} + 2) = 5 x^{4}

= \frac{1}{2 x} (x^{5} + 2) + 5 x^{4} x

Simplify

\frac{1}{2 x} (x^{5} + 2) + 5 x^{4} x : \frac{11 x ^{5} + 2}{2 x}

= \frac{11 x ^{5} + 2}{2 x}

Popular Examples

limit as x approaches 0 of (2x^2+x)^x

x \to 0 lim ((2 x^{2} + x)^{x})

y^{''}+y= 1/((cos(2x))^{3/2)}

y^{^{''}} + y = \frac{1}{( cos ( 2 x ) ) ^{\frac{3}{2}}}

limit as x approaches 2+of (8+x)/(2-x)

x \to 2 + lim (\frac{8 + x}{2 - x})

integral of (10x^2)/(sqrt(1+x^3))

\int \frac{10 x ^{2}}{1 + x ^{3}} d x

y^{^{'}} = - y (3 - t y)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x^5+2) ?
The derivative of sqrt(x)(x^5+2) is (11x^5+2)/(2sqrt(x))
What is the first derivative of sqrt(x)(x^5+2) ?
The first derivative of sqrt(x)(x^5+2) is (11x^5+2)/(2sqrt(x))