derivative of cos^{7/4}(4x^3)

解答

\frac{d}{d x} (cos^{\frac{7}{4}} (4 x^{3}))

- 21 x^{2} sin (4 x^{3}) cos^{\frac{3}{4}} (4 x^{3})

求解步骤

\frac{d}{d x} (cos^{\frac{7}{4}} (4 x^{3}))

使用连锁律:

\frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} \frac{d}{d x} (cos (4 x^{3}))

= \frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} \frac{d}{d x} (cos (4 x^{3}))

\frac{d}{d x} (cos (4 x^{3})) = - sin (4 x^{3}) \cdot 12 x^{2}

= \frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} (- sin (4 x^{3}) \cdot 12 x^{2})

化简

\frac{7 cos ^{\frac{3}{4}} ( 4 x ^{3} )}{4} (- sin (4 x^{3}) \cdot 12 x^{2}) : - 21 x^{2} sin (4 x^{3}) cos^{\frac{3}{4}} (4 x^{3})

= - 21 x^{2} sin (4 x^{3}) cos^{\frac{3}{4}} (4 x^{3})

\int_{1}^{8} x + 1 d x

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

t an g e n t x e^{x}

x \to 0 lim (tan (4 x))

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 9