How do you differentiate #y=sqrt(4+3x)#?
1 Answer
Explanation:
Recall the formula for chain rule:
#color(blue)(bar(ul(|color(white)(a/a)dy/dx=dy/(du)(du)/dxcolor(white)(a/a)|)))# or#color(blue)(bar(ul(|color(white)(a/a)f'(x)=g'[h(x)]h'(x)color(white)(a/a)|)))#
and the formula for power rule:
#color(blue)(bar(ul(|color(white)(a/a)d/dx(x^n)=nx^(n-1)color(white)(a/a)|)))#
To start, recognize the inside and outside functions of
Inside function:
#y=color(darkorange)(4+3x)#
Outside function:#y=color(green)(sqrt(a))#
How to Differentiate Using Chain Rule
#1# . Take the derivative of the outside function,#y=sqrt(a)# , but replace the#a# with the inside function,#4+3x# .
#2# . Multiply by the derivative of the inside function,#4+3x# .
Applying Chain Rule
1. The derivative of the outside function,
#y=sqrt(a)#
#color(red)(darr)#
#y=1/2a^(-1/2)#
#color(red)(darr)#
#y=1/2(4+3x)^(-1/2)#
2.
#y=1/2(4+3x)^(-1/2)#
#color(red)(darr)#
#y=1/2(4+3x)^(-1/2)(3)#
#color(green)(bar(ul(|color(white)(a/a)y=3/(2(4+3x)^(1/2))color(white)(a/a)|)))#