What is the derivative of (x^2(4x+1)) ?

The derivative of (x^2(4x+1)) is 12x^2+2x

What is the first derivative of (x^2(4x+1)) ?

The first derivative of (x^2(4x+1)) is 12x^2+2x

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

12 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 4 x + 1

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

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

\frac{d}{d x} (4 x + 1) = 4

= 2 x (4 x + 1) + 4 x^{2}

Simplify

2 x (4 x + 1) + 4 x^{2} : 12 x^{2} + 2 x

= 12 x^{2} + 2 x

\int \frac{y ^{2} - 36}{y} d y

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

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

\int x \frac{1}{x ^{2}} d x

\frac{d}{d x} (\frac{4 x}{x ^{2} - 2})

What is the derivative of (x^2(4x+1)) ?
The derivative of (x^2(4x+1)) is 12x^2+2x
What is the first derivative of (x^2(4x+1)) ?
The first derivative of (x^2(4x+1)) is 12x^2+2x