What is the derivative of y=x^8f(x) ?

The derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8

What is the first derivative of y=x^8f(x) ?

The first derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8

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derivative of

y = x^{8} f (x)

8 x^{7} f (x) + \frac{df}{d x} x^{8}

Solution steps

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

Apply the Product Rule:

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

f = x^{8}, g = f (x)

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= 8 x^{7} f (x) + \frac{df}{d x} x^{8}

x \to \infty lim (\frac{5 x}{5 x + 3 x ^{\frac{1}{x}}})

\frac{d y}{d x} = x^{9} + 1

\frac{d}{d x} (\frac{( x + b ) ( x - a )}{( x - b )})

\int_{0}^{x^{2}} sin (t^{3}) d t

\frac{d}{d x} (cos (a^{3} + x^{3}))

What is the derivative of y=x^8f(x) ?
The derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8
What is the first derivative of y=x^8f(x) ?
The first derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8