Question

Find derivative y= (6x^2+7)(2x^1/2 -3)

Answer 1

Step-by-step explanation:

the derivative is solved above

Answer 2

Step-by-step explanation:

If y = f(x) × g(x),

then the derivative of y is

$\frac{dy}{dx} = \frac{d \: f(x)}{dx} \times g(x) \: + \frac{d \: g(x)}{dx} \times f(x) \:$

In our case,

f(x) = 6x^2 +7

g(x) = 2√x -3

df(x)/dx = 12x

dg(x)/dx = 1/√x

Put these back in the above equation and solve.

dy/dx = 12x × (2√x -3) + (1/√x)×(6x^2 +7)

=

$24 {x}^{ \frac{3}{2} } - 36x + 6 {x}^{ \frac{3}{2} } + \frac{7}{ \sqrt{x} }$

=

$30 {x}^{ \frac{3}{2} } - 36x + \frac{7}{ \sqrt{x} }$