Question

Tìm đạo hàm của mỗi hàm số sau:

a)     \(y = 4{x^3} - 3{x^2} + 2x + 10\)

b)    \(y = \frac{{x + 1}}{{x - 1}}\)

c)     \(y =  - 2x\sqrt x \)

d)    \(y = 3\sin x + 4\cos x - \tan x\)

e)     \(y = {4^x} + 2{e^x}\)

f)      \(y = x\ln x\)

Answer 1

a: \(y'=4\cdot3x^2-3\cdot2x+2=12x^2-6x+2\)

b: \(y'=\dfrac{\left(x+1\right)'\left(x-1\right)-\left(x+1\right)\left(x-1\right)'}{\left(x-1\right)^2}=\dfrac{x-1-x-1}{\left(x-1\right)^2}=\dfrac{-2}{\left(x-1\right)^2}\)

c: \(y'=-2\cdot\left(\sqrt{x}\cdot x\right)'\)

\(=-2\cdot\left(\dfrac{x+x}{2\sqrt{x}}\right)=-2\cdot\dfrac{2x}{2\sqrt{x}}=-2\sqrt{x}\)

d: \(y'=\left(3sinx+4cosx-tanx\right)\)'

\(=3cosx-4sinx+\dfrac{1}{cos^2x}\)

e: \(y'=\left(4^x+2e^x\right)'\)

\(=4^x\cdot ln4+2\cdot e^x\)

f: \(y'=\left(x\cdot lnx\right)'=lnx+1\)