derivative \sqrt[4]{(2x+x^5)^7}

Lösung

ableitung von

4 (2 x + x^{5})^{7}

\frac{7 ( 2 x + x ^{5} ) ^{6} ( 2 + 5 x ^{4} )}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 (2 x + x^{5})^{7})

Wende die Kettenregel an:

\frac{1}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} ((2 x + x^{5})^{7})

= \frac{1}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} ((2 x + x^{5})^{7})

\frac{d}{d x} ((2 x + x^{5})^{7}) = 7 (2 x + x^{5})^{6} (2 + 5 x^{4})

= \frac{1}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}} \cdot 7 (2 x + x^{5})^{6} (2 + 5 x^{4})

Vereinfache

\frac{1}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}} \cdot 7 (2 x + x^{5})^{6} (2 + 5 x^{4}) : \frac{7 ( 2 x + x ^{5} ) ^{6} ( 2 + 5 x ^{4} )}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}}

= \frac{7 ( 2 x + x ^{5} ) ^{6} ( 2 + 5 x ^{4} )}{4 ( ( 2 x + x ^{5} ) ^{7} ) ^{\frac{3}{4}}}

d er i v a t i v e sec (5 x)

d er i v a t i v e f (x) = 5 x^{2} + 5 x + 7

\frac{\partial}{\partial x} (arctan (\frac{y}{( x - 1 )}))

\frac{\partial}{\partial x} (62 - 2 x^{2} - 2 y^{2})

\frac{d}{d x} (ln (\frac{1}{1 + x}))