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Popular >

derivative of f(x)=x^2(4x^3-1)

Solution

derivative of

f (x) = x^{2} (4 x^{3} - 1)

Solution

20 x^{4} - 2 x

Solution steps

\frac{d}{d x} (x^{2} (4 x^{3} - 1))

Apply the Product Rule:

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

f = x^{2}, g = 4 x^{3} - 1

= \frac{d}{d x} (x^{2}) (4 x^{3} - 1) + \frac{d}{d x} (4 x^{3} - 1) x^{2}

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

\frac{d}{d x} (4 x^{3} - 1) = 12 x^{2}

= 2 x (4 x^{3} - 1) + 12 x^{2} x^{2}

Simplify

2 x (4 x^{3} - 1) + 12 x^{2} x^{2} : 20 x^{4} - 2 x

= 20 x^{4} - 2 x

Popular Examples

integral of (sqrt(x^2-36))/(x^4)

\int \frac{x ^{2} - 36}{x ^{4}} d x

integral from 1 to 2 of (-2x+6)

\int_{1}^{2} (- 2 x + 6) d x

tangent of 3x^2+2 tangent of

3 x^{2} + 2

derivative of y=(x^2+3x)2 derivative of

y = (x^{2} + 3 x) 2

(\partial)/(\partial x)(5x^2+y^2+9)

\frac{\partial}{\partial x} (5 x^{2} + y^{2} + 9)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2(4x^3-1) ?
The derivative of f(x)=x^2(4x^3-1) is 20x^4-2x
What is the first derivative of f(x)=x^2(4x^3-1) ?
The first derivative of f(x)=x^2(4x^3-1) is 20x^4-2x