Find the equation of the tangent line to the graph of f(x)=cos(3x)ln(x^4) at (1,0)

Question

Find the equation of the tangent line to the graph of f(x)=cos(3x)ln(x^4) at (1,0)

Answer 1

First we need to find the slope to the curve at (1,0)

slope = f'(x) = cos(3x)(4x³/x⁴)-3sin(3x)ln(x⁴) = cos(3x)(4/x)-3sin(3x)

f'(1) = m = 4cos(3)-3sin(3) ≈ -4.4

y = m(x-x₀)+y₀ = -4.4(x-1) + 0

y = -4.4x+4.4