Question

tính đạo hàm

a) \(y=\left(x^2-2x\right).3^x\)

b) \(y=\left(x+5\right).sin2x\)

c) \(y=x^3.log_4x\)

Answer 1

a: \(y=\left(x^2-2x\right)\cdot3^x\)

=>\(y'=\left(x^2-2x\right)'\cdot3^x+\left(x^2-2x\right)\cdot\left(3^x\right)'\)

=>\(y'=3^x\left(2x-2\right)+\left(x^2-2x\right)\cdot3^x\cdot ln3\)

b: \(y=\left(x+5\right)\cdot sin2x\)

=>\(y'=\left(x+5\right)'\cdot sin2x+\left(x+5\right)\cdot\left(sin2x\right)'\)

=>\(y'=sin2x+\left(x+5\right)\cdot\left(2x\right)'\cdot cos2x\)

=>\(y'=sin2x+\left(2x+10\right)\cdot cos2x\)

c: \(y=x^3\cdot log_4x\)

=>\(y'=\left(x^3\right)'\cdot log_4x+\left(x^3\right)\cdot\left(log_4x\right)'\)

=>\(y'=3x^2\cdot log_4x+x^3\cdot\dfrac{1}{xln4}=3x^2\cdot log_4x+\dfrac{x^2}{ln4}\)