derivative of 2cos(x^2)

解答

\frac{d}{d x} (2 cos (x^{2}))

- 4 x sin (x^{2})

求解步骤

\frac{d}{d x} (2 cos (x^{2}))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (cos (x^{2}))

使用连锁律:

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

= - sin (x^{2}) \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= 2 (- sin (x^{2}) \cdot 2 x)

化简

= - 4 x sin (x^{2})

x \to 2 - lim (\frac{2 x + 1}{x - 2})

\frac{d}{d x} (x^{2} tanh (\frac{1}{x}))

d er i v a t i v e \frac{( 10 y ^{3} - 9 y ^{2} + 6 y - 10 )}{( 2 y + 3 )}

5 x^{^{''}} + 20 x^{^{'}} + 20 x = 28

\int sin^{3} (x) \cdot cos^{2} (x) d x