What is the derivative of x^6{f}(x) ?

The derivative of x^6{f}(x) is 6x^5{f}(x)+derivative of {f}(x)x^6

What is the first derivative of x^6{f}(x) ?

The first derivative of x^6{f}(x) is 6x^5{f}(x)+derivative of {f}(x)x^6

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\frac{d}{d x} (x^{6} f (x))

6 x^{5} f (x) + \frac{d}{d x} (f (x)) x^{6}

Solution steps

\frac{d}{d x} (x^{6} f (x))

Apply the Product Rule:

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

f = x^{6}, g = f (x)

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= 6 x^{5} f (x) + \frac{d}{d x} (f (x)) x^{6}

f (u) = ln (u)

\int_{0}^{1} (- 12 e^{x}) d x

x \to \infty lim (\frac{- 1}{x})

\frac{d}{d x} (x^{9} f (x))

\frac{d}{d x} (c e^{\frac{x}{6}})

What is the derivative of x^6{f}(x) ?
The derivative of x^6{f}(x) is 6x^5{f}(x)+derivative of {f}(x)x^6
What is the first derivative of x^6{f}(x) ?
The first derivative of x^6{f}(x) is 6x^5{f}(x)+derivative of {f}(x)x^6