derivative f(x)=x^8sqrt(5-3x)

Lösung

ableitung von

f (x) = x^{8} 5 - 3 x

\frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

Schritte zur Lösung

\frac{d}{d x} (x^{8} 5 - 3 x)

Wende die Produktregel an:

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

f = x^{8}, g = 5 - 3 x

= \frac{d}{d x} (x^{8}) 5 - 3 x + \frac{d}{d x} (5 - 3 x) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (5 - 3 x) = - \frac{3}{2 5 - 3 x}

= 8 x^{7} 5 - 3 x + (- \frac{3}{2 5 - 3 x}) x^{8}

Vereinfache

8 x^{7} 5 - 3 x + (- \frac{3}{2 5 - 3 x}) x^{8} : \frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

= \frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

d er i v a t i v e x 4 - x^{2}

d er i v a t i v e f (x) = (x^{2} + 3 x - 2)^{4}

t an g e n t f (x) = sin (2 x) cos (x), at x = π

d er i v a t i v e f (x) = (x^{2} + 1)^{2}

x = - 1