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Popular >

derivative of (1+4x^2(x-x^2))

Solution

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

Solution

- 16 x^{3} + 12 x^{2} - 2 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (1 + 4 x^{2}) = 8 x

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

= 8 x (x - x^{2}) + (1 - 2 x) (1 + 4 x^{2})

Simplify

8 x (x - x^{2}) + (1 - 2 x) (1 + 4 x^{2}) : - 16 x^{3} + 12 x^{2} - 2 x + 1

= - 16 x^{3} + 12 x^{2} - 2 x + 1

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

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(1 + x)^{- \frac{2}{5}}

integral of e^{-kx}cos(wx)

\int e^{- k x} cos (w x) d x

3y^{''}-6y^'+30y=e^xtan(3x)

3 y^{^{''}} - 6 y^{^{'}} + 30 y = e^{x} tan (3 x)

(\partial)/(\partial x)(4x^2+3y^2)

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (1+4x^2(x-x^2)) ?
The derivative of (1+4x^2(x-x^2)) is -16x^3+12x^2-2x+1
What is the first derivative of (1+4x^2(x-x^2)) ?
The first derivative of (1+4x^2(x-x^2)) is -16x^3+12x^2-2x+1