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Beliebt Rechnen >

derivative f(x)=cos(2x)sin(5*x)

Lösung

ableitung von

f (x) = cos (2 \cdot x) \cdot sin (5 \cdot x)

Lösung

- 2 sin (2 x) sin (5 x) + 5 cos (5 x) cos (2 x)

Schritte zur Lösung

\frac{d}{d x} (cos (2 x) sin (5 x))

Wende die Produktregel an:

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

f = cos (2 x), g = sin (5 x)

= \frac{d}{d x} (cos (2 x)) sin (5 x) + \frac{d}{d x} (sin (5 x)) cos (2 x)

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= (- sin (2 x) \cdot 2) sin (5 x) + cos (5 x) \cdot 5 cos (2 x)

Vereinfache

= - 2 sin (2 x) sin (5 x) + 5 cos (5 x) cos (2 x)

Graph

Beliebte Beispiele

derivative of (x^4-1/(x^4+1))

\frac{d}{d x} (\frac{x ^{4} - 1}{x ^{4} + 1})

derivative of (x^4-3x^2+5^3)

\frac{d}{d x} ((x^{4} - 3 x^{2} + 5)^{3})

sum from n=1 to infinity of n/((2n)!)

n = 1 \sum \infty \frac{n}{( 2 n ) !}

derivative f(x)=x^2-8x-8

d er i v a t i v e f (x) = x^{2} - 8 x - 8

(\partial)/(\partial x)(x^6y^8-x^5y^7)

\frac{\partial}{\partial x} (x^{6} y^{8} - x^{5} y^{7})