Answer:
[tex]\frac{dy}{dt}[/tex] = 8
Step-by-step explanation:
Given:
x = x(t) and y = y(t)
Let y = x² + 6
By differentiating the given equation with respect to t,
[tex]\frac{dy}{dt}=\frac{d}{dt}(x^{2}+6)[/tex]
[tex]\frac{dy}{dt}=\frac{d}{dt}(x^{2})+\frac{d}{dt}(6)[/tex]
Since, [tex]\frac{dx}{dt}=4[/tex] when x = 1
[tex]\frac{dy}{dt}=2x\frac{dx}{dt}+\frac{d}{dt}(6)[/tex]
[tex]\frac{dy}{dt}=2(1)(4)+0[/tex] [By substituting the values of [tex]\frac{dx}{dt}[/tex] and x = 1]
[tex]\frac{dy}{dt}[/tex] = 8
