derivative of cos(x^3*3x^2)

解答

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

3 (- 3 x^{4} sin (x^{3}) + 2 x cos (x^{3}))

求解步骤

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

将常数提出:

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

= 3 \frac{d}{d x} (cos (x^{3}) x^{2})

使用微分乘法定则:

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

f = cos (x^{3}), g = x^{2}

= 3 (\frac{d}{d x} (cos (x^{3})) x^{2} + \frac{d}{d x} (x^{2}) cos (x^{3}))

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

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

= 3 ((- sin (x^{3}) \cdot 3 x^{2}) x^{2} + 2 x cos (x^{3}))

化简

3 ((- sin (x^{3}) \cdot 3 x^{2}) x^{2} + 2 x cos (x^{3})) : 3 (- 3 x^{4} sin (x^{3}) + 2 x cos (x^{3}))

= 3 (- 3 x^{4} sin (x^{3}) + 2 x cos (x^{3}))

\int_{0}^{2} (x^{2}) d x

d er i v a t i v e \frac{14 x + 6 x ^{2}}{( 7 + 6 x ) ^{2}}

\int_{0}^{4} π (4 x^{2})^{2} d x

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

\int cos (16 x) cos (7 x) d x