What is the derivative of x^9{f}(x) ?

The derivative of x^9{f}(x) is 9x^8{f}(x)+derivative of {f}(x)x^9

What is the first derivative of x^9{f}(x) ?

The first derivative of x^9{f}(x) is 9x^8{f}(x)+derivative of {f}(x)x^9

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

9 x^{8} f (x) + \frac{d}{d x} (f (x)) x^{9}

Solution steps

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

Apply the Product Rule:

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

f = x^{9}, g = f (x)

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= 9 x^{8} f (x) + \frac{d}{d x} (f (x)) x^{9}

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

\int 4 x^{2} - sin (x) + C d x

\int \frac{1}{x ^{3}} + x d x

\frac{x - 3}{2}

\frac{\partial}{\partial x} (x^{3} y z^{2} + 7 yz)

What is the derivative of x^9{f}(x) ?
The derivative of x^9{f}(x) is 9x^8{f}(x)+derivative of {f}(x)x^9
What is the first derivative of x^9{f}(x) ?
The first derivative of x^9{f}(x) is 9x^8{f}(x)+derivative of {f}(x)x^9