derivative of sinh^3(xsin^2(x))

Lösung

\frac{d}{d x} (sinh^{3} (x) sin^{2} (x))

3 sinh^{2} (x) cosh (x) sin^{2} (x) + sin (2 x) sinh^{3} (x)

Schritte zur Lösung

\frac{d}{d x} (sinh^{3} (x) sin^{2} (x))

Wende die Produktregel an:

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

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

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

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

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

= 3 sinh^{2} (x) cosh (x) sin^{2} (x) + sin (2 x) sinh^{3} (x)

d er i v a t i v e f (x) = 2 cos (x) + cos^{2} (x)

\int \frac{ln ^{2} ( x )}{x ^{2}} d x

n \to 1 lim (3 - \frac{7}{4 ^{n}})

\frac{\partial}{\partial x} (x y^{10} + x^{2} + y^{4})

\int (e^{3 x} + 1) d x