Question

(sqrt(cos(x))cos(400x)+sqrt
(abs(x))-0.4)(4-xx) ^ 0.1

Answer 1

\left(\frac{x}x\right-\frac{\sin \left(x\right)\cos \left(400x\right)}{2\sqrt{\cos \left(x\right)}}-400\sin \left(400x\right)\sqrt{\cos \left(x\right)}\right)\left(4-x^{1.1}\right)+\left(-1.1x^{0.1}\right)\left(\cos \left(400x\right)\sqrt{\cos \left(x\right)}+\sqrtx\right-0.4\right)

Explanation:

\frac{d}{dx}\left(\left(\sqrt{\cos \left(x\right)}\cos \left(400x\right)+\sqrtx\right-0.4\right)\left(4-xx^{0.1}\right)\right)

=\left(\cos \left(400x\right)\sqrt{\cos \left(x\right)}+\sqrtx\right-0.4\right)\left(4-x^{1.1}\right)

=\frac{d}{dx}\left(\cos \left(400x\right)\sqrt{\cos \left(x\right)}+\sqrtx\right-0.4\right)\left(4-x^{1.1}\right)+\frac{d}{dx}\left(4-x^{1.1}\right)\left(\cos \left(400x\right)\sqrt{\cos \left(x\right)}+\sqrtx\right-0.4\right)

=\frac{x}2\left-\frac{\sin \left(x\right)\cos \left(400x\right)}{2\sqrt{\cos \left(x\right)}}-400\sin \left(400x\right)\sqrt{\cos \left(x\right)}