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Popular >

derivative of (x^2+3*sqrt(x))

Solution

\frac{d}{d x} ((x^{2} + 3) \cdot x)

Solution

\frac{5 x ^{2} + 3}{2 x}

Solution steps

\frac{d}{d x} ((x^{2} + 3) x)

Apply the Product Rule:

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

f = x^{2} + 3, g = x

= \frac{d}{d x} (x^{2} + 3) x + \frac{d}{d x} (x) (x^{2} + 3)

\frac{d}{d x} (x^{2} + 3) = 2 x

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

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

Simplify

2 x x + \frac{1}{2 x} (x^{2} + 3) : \frac{5 x ^{2} + 3}{2 x}

= \frac{5 x ^{2} + 3}{2 x}

Popular Examples

derivative of x^2+36 derivative of

x^{2} + 36

limit as x approaches 1+of x^{1/((x-1))}

x \to 1 + lim (x^{\frac{1}{( x - 1 )}})

integral of cos^9(x)tan^3(x)

\int cos^{9} (x) tan^{3} (x) d x

25y^{''}-40y^'+16y=0,y(0)=2,y^'(0)=3

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 3

integral of (24x^2)/(sqrt(36-x^2))

\int \frac{24 x ^{2}}{36 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+3*sqrt(x)) ?
The derivative of (x^2+3*sqrt(x)) is (5x^2+3)/(2sqrt(x))
What is the first derivative of (x^2+3*sqrt(x)) ?
The first derivative of (x^2+3*sqrt(x)) is (5x^2+3)/(2sqrt(x))