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

The derivative of {f}(x(x{f}(x)(x{f}(x)))) is 2x{f}(x)^3+3{f}(x)^2 derivative of {f}(x)x^2

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

The first derivative of {f}(x(x{f}(x)(x{f}(x)))) is 2x{f}(x)^3+3{f}(x)^2 derivative of {f}(x)x^2

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

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

Solution steps

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

Simplify

f (x) (x f (x) (x f (x))) : x^{2} f (x)^{3}

= \frac{d}{d x} (x^{2} f (x)^{3})

Apply the Product Rule:

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

f = x^{2}, g = f (x)^{3}

= \frac{d}{d x} (x^{2}) f (x)^{3} + \frac{d}{d x} (f (x)^{3}) x^{2}

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

\frac{d}{d x} (f (x)^{3}) = 3 f (x)^{2} \frac{d}{d x} (f (x))

= 2 x f (x)^{3} + 3 f (x)^{2} \frac{d}{d x} (f (x)) x^{2}

\frac{d}{d x} (3^{x l n (x)})

lo g_{e} (sin (2 x) + cot (2 x))

y = \frac{1}{2} x

\int_{π}^{2 π} (t - π) e^{- s t} d t

x y^{^{'}} - 2 y = x^{5}

What is the derivative of {f}(x(x{f}(x)(x{f}(x)))) ?
The derivative of {f}(x(x{f}(x)(x{f}(x)))) is 2x{f}(x)^3+3{f}(x)^2 derivative of {f}(x)x^2
What is the first derivative of {f}(x(x{f}(x)(x{f}(x)))) ?
The first derivative of {f}(x(x{f}(x)(x{f}(x)))) is 2x{f}(x)^3+3{f}(x)^2 derivative of {f}(x)x^2