derivative of x^4sec(y)

解答

\frac{d}{d x} (x^{4} sec (y))

4 x^{3} sec (y) + sec (y) tan (y) \frac{d y}{d x} x^{4}

求解步骤

\frac{d}{d x} (x^{4} sec (y))

使用微分乘法定则:

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

f = x^{4}, g = sec (y)

= \frac{d}{d x} (x^{4}) sec (y) + \frac{d}{d x} (sec (y)) x^{4}

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

\frac{d}{d x} (sec (y)) = sec (y) tan (y) \frac{d y}{d x}

= 4 x^{3} sec (y) + sec (y) tan (y) \frac{d y}{d x} x^{4}

x^{6} + y^{5} x^{7} + 3 y^{^{'}} = 0

d er i v a t i v e y = t (ln (2 t))^{2}

t a y l or \frac{1}{3 - x}

\int \frac{- 1}{2} cos (2 x) d x

\frac{d}{d x} (\frac{x}{z ( x )})