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Beliebt Rechnen >

(\partial)/(\partial x)(e^y+x+x^4+5)

Lösung

\frac{\partial}{\partial x} (e^{y} + x + x^{4} + 5)

Lösung

4 x^{3} + 1

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{y} + x + x^{4} + 5)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (e^{y}) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (5)

\frac{\partial}{\partial x} (e^{y}) = 0

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (5) = 0

= 0 + 1 + 4 x^{3} + 0

Vereinfache

= 4 x^{3} + 1

Beliebte Beispiele

fläche 5+2sqrt(x),((15+x))/3

a re a 5 + 2 x, \frac{( 15 + x )}{3}

(\partial)/(\partial x)(2x^2y+4y^3)

\frac{\partial}{\partial x} (2 x^{2} y + 4 y^{3})

derivative y=(x+1/x)(x-1/x+1)

d er i v a t i v e y = (x + \frac{1}{x}) (x - \frac{1}{x} + 1)

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

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

derivative of 2ln(sqrt(x))

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