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Popular >

derivative of y=(1+x^2)(3-2x)

Solution

derivative of

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

Solution

- 6 x^{2} + 6 x - 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (3 - 2 x) + (- 2) (1 + x^{2}) : - 6 x^{2} + 6 x - 2

= - 6 x^{2} + 6 x - 2

Popular Examples

derivative of 5x^3-6x

\frac{d}{d x} (5 x^{3} - 6 x)

sum from n=1 to infinity of 9/(n^2)

n = 1 \sum \infty \frac{9}{n ^{2}}

derivative of (2x^2+8x+8)/(sqrt(x))derivative of

\frac{2 x ^{2} + 8 x + 8}{x}

(\partial)/(\partial x)((xy)^{(1/2)})

\frac{\partial}{\partial x} ((x y)^{(\frac{1}{2})})

integral from 2 to 4 of 3x-6

\int_{2}^{4} 3 x - 6 d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(1+x^2)(3-2x) ?
The derivative of y=(1+x^2)(3-2x) is -6x^2+6x-2
What is the first derivative of y=(1+x^2)(3-2x) ?
The first derivative of y=(1+x^2)(3-2x) is -6x^2+6x-2