What is the derivative of x*g(x)*f(x) ?

The derivative of x*g(x)*f(x) is 3x^2gf

What is the first derivative of x*g(x)*f(x) ?

The first derivative of x*g(x)*f(x) is 3x^2gf

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derivative of

x \cdot g (x) \cdot f (x)

3 x^{2} g f

Solution steps

\frac{d}{d x} (xgx f x)

Simplify

xgx f x : x^{3} g f

= \frac{d}{d x} (x^{3} g f)

Treat

g, f

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= g f \frac{d}{d x} (x^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= g f \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} g f

f (x) = (6 x^{2} - x + 7)^{- \frac{5}{3}}

\frac{d y}{d t} = k (y - 60)

\int \frac{x}{( 4 x + 5 ) ^{2}} d x

x \to 1 lim ((x^{3} + 2) (3 - x))

x \to 3 lim (\frac{( 4 x ^{2} + 3 x )}{5})

What is the derivative of x*g(x)*f(x) ?
The derivative of x*g(x)*f(x) is 3x^2gf
What is the first derivative of x*g(x)*f(x) ?
The first derivative of x*g(x)*f(x) is 3x^2gf