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Beliebt Rechnen >

derivative y=x^5+cos^5(x)

Lösung

ableitung von

y = x^{5} + cos^{5} (x)

Lösung

5 x^{4} - 5 cos^{4} (x) sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{5} + cos^{5} (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{5}) + \frac{d}{d x} (cos^{5} (x))

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (cos^{5} (x)) = - 5 cos^{4} (x) sin (x)

= 5 x^{4} - 5 cos^{4} (x) sin (x)

Graph

Beliebte Beispiele

limit as x approaches 90+of tan(x)

x \to 90 + lim (tan (x))

(dy)/(dx)+(5/x)y=-x+5

\frac{d y}{d x} + (\frac{5}{x}) y = - x + 5

partialfraction x/((2x+3))

p a r t ia l f r a c t i o n \frac{x}{( 2 x + 3 )}

derivative f(x)3x^4(x^2-2x)

d er i v a t i v e f (x) 3 x^{4} (x^{2} - 2 x)

(\partial)/(\partial x)(2/3 (x^2+1)^{3/2})

\frac{\partial}{\partial x} (\frac{2}{3} (x^{2} + 1)^{\frac{3}{2}})