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Popular >

derivative of (x-2(x-3)^2)

Solution

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

Solution

3 x^{2} - 16 x + 21

Solution steps

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

Apply the Product Rule:

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

f = x - 2, g = (x - 3)^{2}

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

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

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

= 1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 2)

Simplify

1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 2) : 3 x^{2} - 16 x + 21

= 3 x^{2} - 16 x + 21

Popular Examples

integral from 0 to pi/6 of 3sec^2(x)

\int_{0}^{\frac{π}{6}} 3 sec^{2} (x) d x

integral of cos^3(1/3)x

\int cos^{3} (\frac{1}{3}) x d x

(dy)/(dx)+1/x y=3cos(2x)

\frac{d y}{d x} + \frac{1}{x} y = 3 cos (2 x)

integral of 1/(1+sqrt(7x))

\int \frac{1}{1 + 7 x} d x

(\partial)/(\partial x)(sqrt(x^2+y^2-2))

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

Frequently Asked Questions (FAQ)

What is the derivative of (x-2(x-3)^2) ?
The derivative of (x-2(x-3)^2) is 3x^2-16x+21
What is the first derivative of (x-2(x-3)^2) ?
The first derivative of (x-2(x-3)^2) is 3x^2-16x+21