derivative of pix^7-2x^5-5x^{-2}

الحلّ

\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

7 π x^{6} - 10 x^{4} + \frac{10}{x ^{3}}

خطوات الحلّ

\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

(f \pm g)^{'} = f^{'} \pm g^{'}

:استعمل قانون الجمع

= \frac{d}{d x} (π x^{7}) - \frac{d}{d x} (2 x^{5}) - \frac{d}{d x} (5 x^{- 2})

\frac{d}{d x} (π x^{7}) = 7 π x^{6}

\frac{d}{d x} (2 x^{5}) = 10 x^{4}

\frac{d}{d x} (5 x^{- 2}) = - \frac{10}{x ^{3}}

= 7 π x^{6} - 10 x^{4} - (- \frac{10}{x ^{3}})

بسّط

= 7 π x^{6} - 10 x^{4} + \frac{10}{x ^{3}}

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

d er i v a t i v e 8 sin (x)

f (x) = x^{\frac{3}{5}}

d er i v a t i v e y = x^{6 x}

\int 8 sin (2) (x) cos (3) (x) d x