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Beliebt Rechnen >

derivative of 2^x(pix^2+cos(x))

Lösung

\frac{d}{d x} (2^{x} (π x^{2} + cos (x)))

Lösung

2^{x} ln (2) (π x^{2} + cos (x)) + (2 π x - sin (x)) \cdot 2^{x}

Schritte zur Lösung

\frac{d}{d x} (2^{x} (π x^{2} + cos (x)))

Wende die Produktregel an:

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

f = 2^{x}, g = π x^{2} + cos (x)

= \frac{d}{d x} (2^{x}) (π x^{2} + cos (x)) + \frac{d}{d x} (π x^{2} + cos (x)) 2^{x}

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

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

= 2^{x} ln (2) (π x^{2} + cos (x)) + (2 π x - sin (x)) \cdot 2^{x}

Graph

Beliebte Beispiele

limit as x approaches 0 of (sin^2(6x))/7

x \to 0 lim (\frac{sin ^{2} ( 6 x )}{7})

inverselaplace 1/(s(s^2-1))

in v erse l a pl a ce \frac{1}{s ( s ^{2} - 1 )}

tangent f(x)= 1/(x+2),\at x=7

t an g e n t f (x) = \frac{1}{x + 2}, at x = 7

derivative f(x)=(x^2)/(x+5)

d er i v a t i v e f (x) = \frac{x ^{2}}{x + 5}

integral from 4 to 9 of 1/(9-sqrt(x))

\int_{4}^{9} \frac{1}{9 - x} d x