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Popular >

derivative of f(x)=x(x+1)^2

Solution

derivative of

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

Solution

3 x^{2} + 4 x + 1

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x + 1)^{2}

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

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

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

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

Simplify

1 \cdot (x + 1)^{2} + 2 (x + 1) x : 3 x^{2} + 4 x + 1

= 3 x^{2} + 4 x + 1

Popular Examples

(\partial)/(\partial x)(2x^2+3y^2-z^2)

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} - z^{2})

tangent of y=4+xsqrt(x),(1,5)tangent of

y = 4 + x x, (1, 5)

limit as x approaches 2 of sqrt(x^4)-8

x \to 2 lim (x^{4} - 8)

y^{''}+y^'-6y=12x-50sin(x)

y^{^{''}} + y^{^{'}} - 6 y = 12 x - 50 sin (x)

(d^2)/(dx^2)(cos(7x))

\frac{d ^{2}}{d x ^{2}} (cos (7 x))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x(x+1)^2 ?
The derivative of f(x)=x(x+1)^2 is 3x^2+4x+1
What is the first derivative of f(x)=x(x+1)^2 ?
The first derivative of f(x)=x(x+1)^2 is 3x^2+4x+1