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Popular >

derivative of g(x)=x^2(1-9x)

Solution

derivative of

g (x) = x^{2} (1 - 9 x)

Solution

2 x - 27 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - 9 x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - 9 x

= \frac{d}{d x} (x^{2}) (1 - 9 x) + \frac{d}{d x} (1 - 9 x) x^{2}

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

\frac{d}{d x} (1 - 9 x) = - 9

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

Simplify

2 x (1 - 9 x) + (- 9) x^{2} : 2 x - 27 x^{2}

= 2 x - 27 x^{2}

Popular Examples

integral of 1/(3-2y-y^2)

\int \frac{1}{3 - 2 y - y ^{2}} d y

(\partial)/(\partial y)(ycos(xy))

\frac{\partial}{\partial y} (y cos (x y))

integral of (e^x)/(5-e^{2x)}

\int \frac{e ^{x}}{5 - e ^{2 x}} d x

limit as x approaches infinity of-3/2 x

x \to \infty lim (- \frac{3}{2} x)

limit as x approaches-2+of (x^2-9)/(x^2-2x-8)

x \to - 2 + lim (\frac{x ^{2} - 9}{x ^{2} - 2 x - 8})

Frequently Asked Questions (FAQ)

What is the derivative of g(x)=x^2(1-9x) ?
The derivative of g(x)=x^2(1-9x) is 2x-27x^2
What is the first derivative of g(x)=x^2(1-9x) ?
The first derivative of g(x)=x^2(1-9x) is 2x-27x^2