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Popular >

derivative of {f}(x(x)^3(x))

Solution

\frac{d}{d x} (f (x) (x)^{3} (x))

Solution

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

Solution steps

\frac{d}{d x} (f (x) (x)^{3} (x))

Simplify

f (x) (x)^{3} (x) : x^{4} f (x)

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

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

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

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x \to 0 lim (\frac{( x + 1 ) ^{5} - 1}{x})

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Frequently Asked Questions (FAQ)

What is the derivative of {f}(x(x)^3(x)) ?
The derivative of {f}(x(x)^3(x)) is 4x^3{f}(x)+derivative of {f}(x)x^4
What is the first derivative of {f}(x(x)^3(x)) ?
The first derivative of {f}(x(x)^3(x)) is 4x^3{f}(x)+derivative of {f}(x)x^4