en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ({f}(x)(3x^2-6x))

Solution

\frac{d}{d x} ((f (x)) (3 x^{2} - 6 x))

Solution

\frac{d}{d x} (f (x)) (3 x^{2} - 6 x) + (6 x - 6) f (x)

Solution steps

\frac{d}{d x} ((f (x)) (3 x^{2} - 6 x))

Apply the Product Rule:

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

f = f (x), g = 3 x^{2} - 6 x

= \frac{d}{d x} (f (x)) (3 x^{2} - 6 x) + \frac{d}{d x} (3 x^{2} - 6 x) f (x)

\frac{d}{d x} (3 x^{2} - 6 x) = 6 x - 6

= \frac{d}{d x} (f (x)) (3 x^{2} - 6 x) + (6 x - 6) f (x)

Popular Examples

expand (e^{3x}+2)^2 expand

(e^{3 x} + 2)^{2}

expand (1+e^{-x})(y^2-1)expand

(1 + e^{- x}) (y^{2} - 1)

expand sqrt(20)expand

20

simplify 1+(1.6K(x+2)(Tx+1))/(x^2+2x+1.64)simplify

1 + \frac{1.6 K ( x + 2 ) ( T x + 1 )}{x ^{2} + 2 x + 1.64}

expand (10(s^2+119))/((s+5)(s^2+10s+169))expand

\frac{10 ( s ^{2} + 119 )}{( s + 5 ) ( s ^{2} + 10 s + 169 )}

Frequently Asked Questions (FAQ)

What is the derivative of ({f}(x)(3x^2-6x)) ?
The derivative of ({f}(x)(3x^2-6x)) is derivative of {f}(x)(3x^2-6x)+(6x-6){f}(x)
What is the first derivative of ({f}(x)(3x^2-6x)) ?
The first derivative of ({f}(x)(3x^2-6x)) is derivative of {f}(x)(3x^2-6x)+(6x-6){f}(x)