What is the derivative of y=x^6f(x) ?

The derivative of y=x^6f(x) is 6x^5f(x)+(df)/(dx)x^6

What is the first derivative of y=x^6f(x) ?

The first derivative of y=x^6f(x) is 6x^5f(x)+(df)/(dx)x^6

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derivative of

y = x^{6} f (x)

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

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

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

e^{x - y} y^{^{'}} = x - 3

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

- 8 e^{π - t}

(x^{3} + 2 x^{2})^{- 1}

n = 1 \sum \infty arctan (n + 1)

What is the derivative of y=x^6f(x) ?
The derivative of y=x^6f(x) is 6x^5f(x)+(df)/(dx)x^6
What is the first derivative of y=x^6f(x) ?
The first derivative of y=x^6f(x) is 6x^5f(x)+(df)/(dx)x^6