derivative f(x)=5e^x(cos(x)-sin(x))

Lösung

ableitung von

f (x) = 5 e^{x} (cos (x) - sin (x))

- 10 e^{x} sin (x)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = e^{x}, g = cos (x) - sin (x)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

= 5 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x})

Vereinfache

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

= - 10 e^{x} sin (x)

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{0.5})

y^{^{''}} = 1

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

x \to 2 - lim (x + 7)

\frac{\partial}{\partial x} (20 - (3 x^{2} + y^{2}))