derivative of f(1/3 x^3)=2x^5

Lösung

\frac{d}{d x} (f (\frac{1}{3} x^{3})) = 2 x^{5}

f (x) = x^{3} + \frac{c _{1}}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (f (x) (\frac{1}{3} x^{3})) = 2 x^{5}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

f (x) \frac{1}{3} x^{3} = \int 2 x^{5} d x

\int 2 x^{5} d x = \frac{x ^{6}}{3} + c_{1}

f (x) \frac{1}{3} x^{3} = \frac{x ^{6}}{3} + c_{1}

Isoliere

f (x) : f (x) = x^{3} + \frac{3 c _{1}}{x ^{3}}

f (x) = x^{3} + \frac{3 c _{1}}{x ^{3}}

Vereinfache

f (x) = x^{3} + \frac{c _{1}}{x ^{3}}

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

y^{^{'}} = \frac{y ^{4} x ^{4} + 4 x ^{4}}{y ^{3}}

\int \frac{x + 7}{x ^{2} ( x + 2 )} d x

\frac{d}{d x} (\frac{cos ( x ) 2 x ^{3}}{e ^{x}})

x \to + \frac{1}{5} lim (2 + ∣ 5 x - 1 ∣)