What is the derivative of y=x^4f(x) ?

The derivative of y=x^4f(x) is 4x^3f(x)+(df)/(dx)x^4

What is the first derivative of y=x^4f(x) ?

The first derivative of y=x^4f(x) is 4x^3f(x)+(df)/(dx)x^4

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derivative of

y = x^{4} f (x)

4 x^{3} f (x) + \frac{df}{d x} x^{4}

Solution steps

\frac{d}{d x} (x^{4} f (x))

Apply the Product Rule:

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

f = x^{4}, g = f (x)

= \frac{d}{d x} (x^{4}) f (x) + \frac{df}{d x} x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= 4 x^{3} f (x) + \frac{df}{d x} x^{4}

\int \frac{1}{x ( 1 + ln ( x ) ) ^{4}} d x

\frac{6}{2 s + 1}

\int cot (x) ln (sin (x)) d x

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

\frac{d y}{d x} = - y^{\frac{1}{3}}

What is the derivative of y=x^4f(x) ?
The derivative of y=x^4f(x) is 4x^3f(x)+(df)/(dx)x^4
What is the first derivative of y=x^4f(x) ?
The first derivative of y=x^4f(x) is 4x^3f(x)+(df)/(dx)x^4