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

The derivative of x^4f(x) is 5x^4f

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

The first derivative of x^4f(x) is 5x^4f

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derivative of

x^{4} f (x)

5 x^{4} f

Solution steps

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

Simplify

x^{4} f x : x^{5} f

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

Treat

f

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= f \cdot 5 x^{5 - 1}

Simplify

= 5 x^{4} f

(\frac{d y}{d x}) - 3 y = e^{2 x}

y^{^{''}} + 4 y^{^{'}} = 6 e^{- 3 t}

\frac{d y}{d x} + \frac{9 y}{1000 + x} = 0.405

f (x) = 3 sin (x), at x = \frac{π}{4}

f (x) = x^{2} - 4 x + 3, at x = 1

What is the derivative of x^4f(x) ?
The derivative of x^4f(x) is 5x^4f
What is the first derivative of x^4f(x) ?
The first derivative of x^4f(x) is 5x^4f