derivative sin(5xln(x))(sin^2(5x))

Lösung

ableitung von

sin (5 x ln (x)) (sin^{2} (5 x))

cos (5 x ln (x)) \cdot 5 (ln (x) + 1) sin^{2} (5 x) + 5 sin (10 x) sin (5 x ln (x))

Schritte zur Lösung

\frac{d}{d x} (sin (5 x ln (x)) sin^{2} (5 x))

Wende die Produktregel an:

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

f = sin (5 x ln (x)), g = sin^{2} (5 x)

= \frac{d}{d x} (sin (5 x ln (x))) sin^{2} (5 x) + \frac{d}{d x} (sin^{2} (5 x)) sin (5 x ln (x))

\frac{d}{d x} (sin (5 x ln (x))) = cos (5 x ln (x)) \cdot 5 (ln (x) + 1)

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= cos (5 x ln (x)) \cdot 5 (ln (x) + 1) sin^{2} (5 x) + 5 sin (10 x) sin (5 x ln (x))

d er i v a t i v e 3 x^{2} - 3

\int_{5}^{7} x d x

\int_{- 1}^{1} 1 - ∣ x ∣ d x

\int 2 e^{2 t} d t

x \cdot y^{^{''}} + y^{^{'}} = 0