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Beliebt Rechnen >

(\partial)/(\partial x)(5xsin(3x^2y))

Lösung

\frac{\partial}{\partial x} (5 x sin (3 x^{2} y))

Lösung

5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x sin (3 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 \frac{\partial}{\partial x} (x sin (3 x^{2} y))

Wende die Produktregel an:

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

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

= 5 (\frac{\partial}{\partial x} (x) sin (3 x^{2} y) + \frac{\partial}{\partial x} (sin (3 x^{2} y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (3 x^{2} y)) = cos (3 x^{2} y) \cdot 6 y x

= 5 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx)

Vereinfache

5 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx) : 5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

= 5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

Beliebte Beispiele

tangent f(x)=sqrt(x^2-x+13),\at x=4

t an g e n t f (x) = x^{2} - x + 13, at x = 4

integral of (x^2)/(x^3)+5

\int \frac{x ^{2}}{x ^{3}} + 5 d x

derivative r/(sqrt(r^2+3))

d er i v a t i v e \frac{r}{r ^{2} + 3}

laplacetransform 8sin(t)

l a pl a ce t r an s f or m 8 sin (t)

sum from k=1 to infinity of (k^3)/(5^k)

k = 1 \sum \infty \frac{k ^{3}}{5 ^{k}}