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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(y+(cos^2(x))))

Lösung

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

Lösung

- \frac{cos ( x ) sin ( x )}{y + cos ^{2} ( x )}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 y + cos ^{2} ( x )} \frac{\partial}{\partial x} (y + cos^{2} (x))

= \frac{1}{2 y + cos ^{2} ( x )} \frac{\partial}{\partial x} (y + cos^{2} (x))

\frac{\partial}{\partial x} (y + cos^{2} (x)) = - 2 cos (x) sin (x)

= \frac{1}{2 y + cos ^{2} ( x )} (- 2 cos (x) sin (x))

Vereinfache

\frac{1}{2 y + cos ^{2} ( x )} (- 2 cos (x) sin (x)) : - \frac{cos ( x ) sin ( x )}{y + cos ^{2} ( x )}

= - \frac{cos ( x ) sin ( x )}{y + cos ^{2} ( x )}

Beliebte Beispiele

limit as x approaches 2 of sin(x)

x \to 2 lim (sin (x))

derivative of sin^2(e^{3x+1})

\frac{d}{d x} (sin^{2} (e^{3 x + 1}))

sum from n=0 to infinity of (3^n)/(3^n)

n = 0 \sum \infty \frac{3 ^{n}}{3 ^{n}}

integral of (x^3)/(x^4-3)

\int \frac{x ^{3}}{x ^{4} - 3} d x

integral from 0 to 2 of x^2-1

\int_{0}^{2} x^{2} - 1 d x