Question

find differentiation of y=4e^x²-2x by chain rule method.​

Answer 1

y=4e^(x²-2x)

dy/dx = 4 d/dx {e^(x²-2x)}

= 4. e^(x^2 - 2x) . d/dx(x^2 - 2x)

= 4. e^(x^2 - 2x) . (2x - 2)

= 4. (2x - 2) . e^(x^2 - 2x)

= (8x - 8) . e^(x^2 - 2x) (ans.)

Answer 2

Answer: Differentiation by chain rule of $y = 4 e^{x^2-2x}$ is $y =8(x-1)e^{x^2-2x}$

Explanation: Differentiation by chain rule states that  the derivative of f(g(x)) is f'(g(x))⋅g'(x)

$y = 4 e^{x^2-2x}$

$\frac{dy}{dx}= 4\frac{d(e^{x^2-2x})}{dx}$

$\frac{dy}{dx}= 4.e^{x^2-2x}.\frac{d(x^2-2x)}{dx}$

$= 4.e^{x^2-2x}.(2x-2)$

$=8(x-1)e^{x^2-2x}$