derivative of (17-(13-2x^4^7)^3)

Lösung

\frac{d}{d x} ((17 - (13 - 2 x^{4})^{7})^{3})

3 (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{2} (3584 x^{27} - 139776 x^{23} + 2271360 x^{19} - 19685120 x^{15} + 95964960 x^{11} - 249508896 x^{7} + 270301304 x^{3})

Schritte zur Lösung

\frac{d}{d x} ((17 - (13 - 2 x^{4})^{7})^{3})

Vereinfache

(17 - (13 - 2 x^{4})^{7})^{3} : (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{3}

= \frac{d}{d x} ((128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{3})

Wende die Kettenregel an:

3 (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{2} \frac{d}{d x} (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)

= 3 (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{2} \frac{d}{d x} (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)

\frac{d}{d x} (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500) = 3584 x^{27} - 139776 x^{23} + 2271360 x^{19} - 19685120 x^{15} + 95964960 x^{11} - 249508896 x^{7} + 270301304 x^{3}

= 3 (128 x^{28} - 5824 x^{24} + 113568 x^{20} - 1230320 x^{16} + 7997080 x^{12} - 31188612 x^{8} + 67575326 x^{4} - 62748500)^{2} (3584 x^{27} - 139776 x^{23} + 2271360 x^{19} - 19685120 x^{15} + 95964960 x^{11} - 249508896 x^{7} + 270301304 x^{3})

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

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

\int_{1}^{3} (2 x + 1) d x

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

\int \frac{1}{sec ^{4} ( \frac{1}{4} β )} d β