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Beliebt Rechnen >

(\partial)/(\partial y)(xyz^2tan(yt))

Lösung

\frac{\partial}{\partial y} (x y z^{2} tan (y t))

Lösung

x z^{2} (tan (y t) + y t sec^{2} (y t))

Schritte zur Lösung

\frac{\partial}{\partial y} (x y z^{2} tan (y t))

Behandle

x, z, t

als Konstanten

Entferne die Konstante:

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

= x z^{2} \frac{\partial}{\partial y} (y tan (y t))

Wende die Produktregel an:

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

f = y, g = tan (y t)

= x z^{2} (\frac{\partial}{\partial y} (y) tan (y t) + \frac{\partial}{\partial y} (tan (y t)) y)

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

\frac{\partial}{\partial y} (tan (y t)) = sec^{2} (y t) t

= x z^{2} (1 \cdot tan (y t) + sec^{2} (y t) t y)

Vereinfache

= x z^{2} (tan (y t) + y t sec^{2} (y t))

Beliebte Beispiele

tangent y=sqrt(2-6x),\at x=-1

t an g e n t y = 2 - 6 x, at x = - 1

inverselaplace s/(s^2-3)

in v erse l a pl a ce \frac{s}{s ^{2} - 3}

integral from 0 to 3 of 3/2 xsqrt(x+1)

\int_{0}^{3} \frac{3}{2} x x + 1 d x

integral from 2 to 8 of-sqrt(x/2)

\int_{2}^{8} - \frac{x}{2} d x

integral of (cos(ln(9t)))/t

\int \frac{cos ( ln ( 9 t ) )}{t} d t