derivative f(x)=8x^4tan(x)

Lösung

ableitung von

f (x) = 8 x^{4} tan (x)

8 (4 x^{3} tan (x) + sec^{2} (x) x^{4})

Schritte zur Lösung

\frac{d}{d x} (8 x^{4} tan (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x^{4} tan (x))

Wende die Produktregel an:

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

f = x^{4}, g = tan (x)

= 8 (\frac{d}{d x} (x^{4}) tan (x) + \frac{d}{d x} (tan (x)) x^{4})

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

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

= 8 (4 x^{3} tan (x) + sec^{2} (x) x^{4})

x \to 1 lim (ln (x + 1))

\frac{d}{d y} (\frac{1}{2} ln (x^{2} + y^{2}))

n = 1 \sum \infty \frac{2 ^{n} x ^{2 n}}{3 ^{n + 1}}

\frac{\partial}{\partial x} (4 arctan (\frac{3}{x}))

t an g e n t f (x) = 4 + 5 x^{2}, (0, 4)