derivative of cos(5x^2-7x(10x-7))

Lösung

\frac{d}{d x} (cos (5 x^{2} - 7 x) (10 x - 7))

- sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

Schritte zur Lösung

\frac{d}{d x} (cos (5 x^{2} - 7 x) (10 x - 7))

Wende die Produktregel an:

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

f = cos (5 x^{2} - 7 x), g = 10 x - 7

= \frac{d}{d x} (cos (5 x^{2} - 7 x)) (10 x - 7) + \frac{d}{d x} (10 x - 7) cos (5 x^{2} - 7 x)

\frac{d}{d x} (cos (5 x^{2} - 7 x)) = - sin (5 x^{2} - 7 x) (10 x - 7)

\frac{d}{d x} (10 x - 7) = 10

= (- sin (5 x^{2} - 7 x) (10 x - 7)) (10 x - 7) + 10 cos (5 x^{2} - 7 x)

Vereinfache

(- sin (5 x^{2} - 7 x) (10 x - 7)) (10 x - 7) + 10 cos (5 x^{2} - 7 x) : - sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

= - sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

\int (- 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 x^{2}) d x

\frac{\partial}{\partial z} (sin (y))

\frac{d y}{d x} = \frac{( y + x )}{( y - x )}, y (0) = 1

\int \frac{10 X}{X ^{4} - 13 X ^{2} + 36} d X

d er i v a t i v e x^{\frac{8}{x}}