derivative y=\sqrt[4]{(cos(x))^3}

Lösung

ableitung von

y = 4 (cos (x))^{3}

- \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 (cos (x))^{3})

Wende die Kettenregel an:

\frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} ((cos (x))^{3})

= \frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} ((cos (x))^{3})

\frac{d}{d x} ((cos (x))^{3}) = - 3 cos^{2} (x) sin (x)

= \frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} (- 3 cos^{2} (x) sin (x))

Vereinfache

\frac{1}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}} (- 3 cos^{2} (x) sin (x)) : - \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

= - \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

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

d er i v a t i v e f (x) = a^{4} + cos^{4} (x)

\int_{0}^{1} 2 π (2 - y) (4 y^{2}) d y

\int - sin (d) x d x

\int_{0}^{1} 4 x d x