de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial}{\partial x}(4e^{\frac{x^2)/y}-cos(xy^3))

Lösung

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}} - cos (x y^{3}))

Lösung

\frac{8 e ^{\frac{x ^{2}}{y}} x}{y} + y^{3} sin (x y^{3})

Schritte zur Lösung

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}} - cos (x y^{3}))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}}) - \frac{\partial}{\partial x} (cos (x y^{3}))

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}}) = \frac{8 e ^{\frac{x ^{2}}{y}} x}{y}

\frac{\partial}{\partial x} (cos (x y^{3})) = - sin (x y^{3}) y^{3}

= \frac{8 e ^{\frac{x ^{2}}{y}} x}{y} - (- sin (x y^{3}) y^{3})

Vereinfache

= \frac{8 e ^{\frac{x ^{2}}{y}} x}{y} + y^{3} sin (x y^{3})

Beliebte Beispiele

limit as x approaches 0 of 4sqrt(x)+x

x \to 0 lim (4 x + x)

integral of 2x^7+4x^6+x^5+1

\int 2 x^{7} + 4 x^{6} + x^{5} + 1 d x

tangent y=2x^3-2x,(-1,0)

t an g e n t y = 2 x^{3} - 2 x, (- 1, 0)

derivative cos^2(5pix)

d er i v a t i v e cos^{2} (5 π x)

derivative (5ln(4x))/(2-3x)

d er i v a t i v e \frac{5 ln ( 4 x )}{2 - 3 x}