What is the equation of the tangent line of #f(x) =(e^x-x)(e^x-x^2)# at #x=4#? Calculus Derivatives Tangent Line to a Curve 1 Answer Sonnhard Jun 22, 2018 #y_T=(48-29e^4+2e^8)x-128+96e^4-7e^8# Explanation: #f'(x)=2e^(2x)-e^x-3xe^x-e^xx^2+3x^2# #f'(4)=48-29e^4+2e^8# #f(4)=(-16+e^4)(e^4-4)# Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve #3y^2-2x^2=1#? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 1181 views around the world You can reuse this answer Creative Commons License