THe given equation is
[tex] y=(1+4x)^{12} [/tex]
Differentiating using chain rule
[tex] dy/dx = 4*12(1+4x)^{11} = 48(1+4x)^{11} [/tex]
At point (0,1), we will get
[tex] dy/dx = 48(1+4(0))^{11} = 48 [/tex]
Now we use point slope form, which is
[tex] y-y_{1} = m (x-x_{1}) [/tex]
Substituting the values of m, and x1,y1, we will get
[tex] y-1=48(x-0) [/tex]
[tex] y = 48x+1 [/tex]
And that's the required answer .
