derivative f(x)=x^2sin(x^2+3)

Lösung

ableitung von

f (x) = x^{2} sin (x^{2} + 3)

2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin (x^{2} + 3))

Wende die Produktregel an:

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

f = x^{2}, g = sin (x^{2} + 3)

= \frac{d}{d x} (x^{2}) sin (x^{2} + 3) + \frac{d}{d x} (sin (x^{2} + 3)) x^{2}

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

\frac{d}{d x} (sin (x^{2} + 3)) = cos (x^{2} + 3) \cdot 2 x

= 2 x sin (x^{2} + 3) + cos (x^{2} + 3) \cdot 2 x x^{2}

cos (x^{2} + 3) \cdot 2 x x^{2} = 2 x^{3} cos (x^{2} + 3)

= 2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

d er i v a t i v e g (t) = t t 3 t

\int \frac{x ^{2} - 9}{x ^{2}} d x

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{4}{x ^{2}}) y = 0

\frac{d}{d a} (\frac{π ( 9 a ^{2} + 6 a + 1 )}{36 a})

n = 0 \sum \infty 1.0 5^{n}