43. Find an equation of the tangent line to the curve y=10^(x) at the point (1,10)

Question

43. Find an equation of the tangent line to the curve
`y=10^(x)` at the point (1,10)

Answer 1

23x-y=13

Explanation:

we need to find the derivative with respect to x

In(y) =In(10^x)

In(y)=xIn(10)

now we have to take the derivative with respect to x

Therefore, y'=yIn(10)

where y'=10^xIn(10), Chain rule!

note: First derivative function always give us the gradient value when x value is substituted in

Therefore, at x=1, our gradient will be m= 10^1In(10)

Gradient m=23.0 to the nearest tenth

Finding the equation of the line

y-y1=m(x-x1)

y-10=23(x-1)

y-10=23x-23

y-23x=-23+10

y - 23x = -13

so, the equation of the line tangent line is

23x - y =13