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

The derivative of f(x)=(1+4x^2)(x-x^2) is -16x^3+12x^2-2x+1

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

The first derivative of f(x)=(1+4x^2)(x-x^2) is -16x^3+12x^2-2x+1

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derivative of

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

- 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

y = (1 + 2 x)^{9}

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

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

\int_{0}^{4} x (4 x - x^{2}) d x

\int x^{5} e^{2 x^{3}} d x

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