What is the derivative of (x^3+2x^2/(sqrt(x))) ?

The derivative of (x^3+2x^2/(sqrt(x))) is (3sqrt(x)(x+2))/2+x^{3/2}

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

The first derivative of (x^3+2x^2/(sqrt(x))) is (3sqrt(x)(x+2))/2+x^{3/2}

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int sin^{4} (5 θ) d θ

y = (cos (3 x))^{x}

x \to 0 lim (\frac{sin ( 4 x )}{x})

\frac{d}{d x} (A cos (2 x))

\int sin (nπ x) d x

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