What is the derivative of {f}(x{f}(x)(x^2)) ?

The derivative of {f}(x{f}(x)(x^2)) is 2x{f}(x)^2+2{f}(x) derivative of {f}(x)x^2

What is the first derivative of {f}(x{f}(x)(x^2)) ?

The first derivative of {f}(x{f}(x)(x^2)) is 2x{f}(x)^2+2{f}(x) derivative of {f}(x)x^2

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\frac{d}{d x} (f (x) f (x) (x^{2}))

2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}

Solution steps

\frac{d}{d x} (f (x) f (x) (x^{2}))

Simplify

f (x) f (x) (x^{2}) : x^{2} f (x)^{2}

= \frac{d}{d x} (x^{2} f (x)^{2})

Apply the Product Rule:

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

f = x^{2}, g = f (x)^{2}

= \frac{d}{d x} (x^{2}) f (x)^{2} + \frac{d}{d x} (f (x)^{2}) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (f (x)^{2}) = 2 f (x) \frac{d}{d x} (f (x))

= 2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}

x \to 2 lim (\frac{x - 4}{x - 2})

x \to - \infty lim (x^{3} + x)

\frac{d}{d x} (\frac{tan ( x )}{cos ( x ) - 4})

n = 1 \sum \infty - \frac{5}{2 ^{n - 1}}

x \to \infty lim (3)

What is the derivative of {f}(x{f}(x)(x^2)) ?
The derivative of {f}(x{f}(x)(x^2)) is 2x{f}(x)^2+2{f}(x) derivative of {f}(x)x^2
What is the first derivative of {f}(x{f}(x)(x^2)) ?
The first derivative of {f}(x{f}(x)(x^2)) is 2x{f}(x)^2+2{f}(x) derivative of {f}(x)x^2