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Popular >

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

Solution

derivative of

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

Solution

- 8 x^{3} + 6 x^{2} - 2 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 x (x - x^{2}) + (1 - 2 x) (1 + 2 x^{2}) : - 8 x^{3} + 6 x^{2} - 2 x + 1

= - 8 x^{3} + 6 x^{2} - 2 x + 1

Popular Examples

integral from 0 to 5 of 2pi(6-x)(25-x^2)

\int_{0}^{5} 2 π (6 - x) (25 - x^{2}) d x

derivative of arcsin(cos(x^6))derivative of

arcsin (cos (x^{6}))

derivative of log_{2x+1}(2x+3)

\frac{d}{d x} (lo g_{2 x + 1} (2 x + 3))

limit as h approaches 0 of (6xh+3h^2)/h

h \to 0 lim (\frac{6 x h + 3 h ^{2}}{h})

(\partial)/(\partial x)(3e^{x^3y^3})

\frac{\partial}{\partial x} (3 e^{x^{3} y^{3}})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(1+2x^2)(x-x^2) ?
The derivative of f(x)=(1+2x^2)(x-x^2) is -8x^3+6x^2-2x+1
What is the first derivative of f(x)=(1+2x^2)(x-x^2) ?
The first derivative of f(x)=(1+2x^2)(x-x^2) is -8x^3+6x^2-2x+1