Let y=tan(3x+3).Find the differential dy when x=5 and dx=0.3 Find the differential dy when x=5 and dx=0.6

Question

Let .Find the differential  when  and    Find the differential  when  and 

Answer 1

d(tanx)/dx =(1/cos² x), dx=d(3x+3)/3, as derivative of constant is zero and d3x=3dx

d[tan(3x+3)]/dx= 3d[tan(3x+3)]/d(3x+3)= 3/cos²(3x+3)

After that, just substitute value of x in derived equation.

 For example, if x=5 dy=3/ cos²(3*5+3)= 3/ cos²(18)=3/(0.66)²=6.88