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Popular >

derivative of f(x)=x^2(1-4x)

Solution

derivative of

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

Solution

2 x - 12 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 2 x - 12 x^{2}

Popular Examples

tangent of f(x)=x^3-6x^2-34x+40,\at x=-3 tangent of

f (x) = x^{3} - 6 x^{2} - 34 x + 40, at x = - 3

integral from 0 to 7 of xsqrt(49-x^2)

\int_{0}^{7} x 49 - x^{2} d x

integral from 0 to 2 of x(x^2-1)^3

\int_{0}^{2} x (x^{2} - 1)^{3} d x

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

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

sum from n=3 to infinity of 1/(n(n+1))

n = 3 \sum \infty \frac{1}{n ( n + 1 )}

Frequently Asked Questions (FAQ)

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