What is the derivative of {f}(x((x^4)/4-1/4)) ?

The derivative of {f}(x((x^4)/4-1/4)) is ((x^4-1) derivative of {f}(x))/4+x^3{f}(x)

What is the first derivative of {f}(x((x^4)/4-1/4)) ?

The first derivative of {f}(x((x^4)/4-1/4)) is ((x^4-1) derivative of {f}(x))/4+x^3{f}(x)

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\frac{d}{d x} (f (x) (\frac{x ^{4}}{4} - \frac{1}{4}))

\frac{( x ^{4} - 1 ) \frac{d}{d x} ( f ( x ) )}{4} + x^{3} f (x)

Solution steps

\frac{d}{d x} (f (x) (\frac{x ^{4}}{4} - \frac{1}{4}))

Apply the Product Rule:

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

f = f (x), g = \frac{x ^{4}}{4} - \frac{1}{4}

= \frac{d}{d x} (f (x)) (\frac{x ^{4}}{4} - \frac{1}{4}) + \frac{d}{d x} (\frac{x ^{4}}{4} - \frac{1}{4}) f (x)

\frac{d}{d x} (\frac{x ^{4}}{4} - \frac{1}{4}) = x^{3}

= \frac{d}{d x} (f (x)) (\frac{x ^{4}}{4} - \frac{1}{4}) + x^{3} f (x)

Simplify

\frac{d}{d x} (f (x)) (\frac{x ^{4}}{4} - \frac{1}{4}) + x^{3} f (x) : \frac{( x ^{4} - 1 ) \frac{d}{d x} ( f ( x ) )}{4} + x^{3} f (x)

= \frac{( x ^{4} - 1 ) \frac{d}{d x} ( f ( x ) )}{4} + x^{3} f (x)

lo g_{3} (x - 4 x^{2})

\frac{d}{d x} (\frac{1}{( x ^{3} + 4 ) ^{2}})

x \to 0 - lim (x ln (x))

\int_{3}^{8} (x^{3} - π x^{2}) d x

n = 0 \sum \infty 9 ((\frac{5}{12})^{n})

What is the derivative of {f}(x((x^4)/4-1/4)) ?
The derivative of {f}(x((x^4)/4-1/4)) is ((x^4-1) derivative of {f}(x))/4+x^3{f}(x)
What is the first derivative of {f}(x((x^4)/4-1/4)) ?
The first derivative of {f}(x((x^4)/4-1/4)) is ((x^4-1) derivative of {f}(x))/4+x^3{f}(x)