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Popular >

derivative of (x^3+x^2/x)

Solution

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

Solution

2 x + 1

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x, g = x + 1

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x + 1) + 1 \cdot x

Simplify

1 \cdot (x + 1) + 1 \cdot x : 2 x + 1

= 2 x + 1

Popular Examples

integral from 0 to pi of 22sin^4(x)

\int_{0}^{π} 22 sin^{4} (x) d x

integral of (4x^2)/(sqrt(4-x^2))

\int \frac{4 x ^{2}}{4 - x ^{2}} d x

integral of 3/2 t^2

\int \frac{3}{2} t^{2} d t

tangent of f(x)=-3x^2-2,\at x=5 tangent of

f (x) = - 3 x^{2} - 2, at x = 5

integral of-4xe^{x^2}

\int - 4 x e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+x^2/x) ?
The derivative of (x^3+x^2/x) is 2x+1
What is the first derivative of (x^3+x^2/x) ?
The first derivative of (x^3+x^2/x) is 2x+1