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Popular >

derivative of f(x)=x^2*(x^3+2)

Solution

derivative of

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

Solution

5 x^{4} + 4 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{3} + 2) + 3 x^{2} x^{2} : 5 x^{4} + 4 x

= 5 x^{4} + 4 x

Popular Examples

(dy)/(dx)=(16sqrt(x))/(e^y)

\frac{d y}{d x} = \frac{16 x}{e ^{y}}

y^{''}+4y=12sin(2x)

y^{^{''}} + 4 y = 12 sin (2 x)

derivative of f(x)= 4/(3x^2)+1/(x^{2.1)}derivative of

f (x) = \frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}}

integral of ((8+x+x^2))/(sqrt(x))

\int \frac{( 8 + x + x ^{2} )}{x} d x

limit as x approaches 4-of (6x)/(x-4)

x \to 4 - lim (\frac{6 x}{x - 4})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2*(x^3+2) ?
The derivative of f(x)=x^2*(x^3+2) is 5x^4+4x
What is the first derivative of f(x)=x^2*(x^3+2) ?
The first derivative of f(x)=x^2*(x^3+2) is 5x^4+4x