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Beliebt Rechnen >

derivative of 5e^x(cos(x-x))

Lösung

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

Lösung

5 (e^{x} (cos (x) - x) + (- sin (x) - 1) e^{x})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (cos (x) - x) = - sin (x) - 1

= 5 (e^{x} (cos (x) - x) + (- sin (x) - 1) e^{x})

Graph

Beliebte Beispiele

derivative 3/5 x^{5/3}-3/4 x^{1/3}+6

d er i v a t i v e \frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 6

derivative e-e^x+x^e

d er i v a t i v e e - e^{x} + x^{e}

integral of (2+x^8)^48x^7

\int (2 + x^{8})^{4} 8 x^{7} d x

integral of 1/(e^x+e^{-x)+2}

\int \frac{1}{e ^{x} + e ^{- x} + 2} d x

8 y^{^{''}} + y^{^{'}} = 0