derivative xsqrt(7-x^2)

Lösung

ableitung von

x 7 - x^{2}

\frac{- 2 x ^{2} + 7}{7 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x 7 - x^{2})

Wende die Produktregel an:

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

f = x, g = 7 - x^{2}

= \frac{d x}{d x} 7 - x^{2} + \frac{d}{d x} (7 - x^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (7 - x^{2}) = - \frac{x}{7 - x ^{2}}

= 1 \cdot 7 - x^{2} + (- \frac{x}{7 - x ^{2}}) x

Vereinfache

1 \cdot 7 - x^{2} + (- \frac{x}{7 - x ^{2}}) x : \frac{- 2 x ^{2} + 7}{7 - x ^{2}}

= \frac{- 2 x ^{2} + 7}{7 - x ^{2}}

\int (18 x + 2) d x

\int_{0}^{2} \frac{2}{y ^{2} + y - 20} d y

d er i v a t i v e f (x) = - 8 x^{3}

\int \frac{x ^{2} + 7 x + 1}{( x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial y} (2 x y^{4} - 3)