Need a bit of help with derivatives! If you would show work it would be so appre

Question

Need a bit of help with derivatives! If you would show work it would be so appreciated!
1) If F(x) = 5x/(1+x^2), find F'(2) and use it to find an equation of the tangent line to the curve y=5x/(1+x^2) at the point (2,2).
2) Find f'(a) F(t)= 2t+1/t+3
3) the displacement (in meters) of a particle moving in a straight line is given by the equation of motion s=1/t^2 where t is measured in seconds. Find the velocity of the particle at times t=a, t=1, t=2, t=3
Thanks! Need a bit of help with derivatives! If you would show work it would be so appreciated!
1) If F(x) = 5x/(1+x^2), find F'(2) and use it to find an equation of the tangent line to the curve y=5x/(1+x^2) at the point (2,2).
2) Find f'(a) F(t)= 2t+1/t+3
3) the displacement (in meters) of a particle moving in a straight line is given by the equation of motion s=1/t^2 where t is measured in seconds. Find the velocity of the particle at times t=a, t=1, t=2, t=3
Thanks!
1) If F(x) = 5x/(1+x^2), find F'(2) and use it to find an equation of the tangent line to the curve y=5x/(1+x^2) at the point (2,2).
2) Find f'(a) F(t)= 2t+1/t+3
3) the displacement (in meters) of a particle moving in a straight line is given by the equation of motion s=1/t^2 where t is measured in seconds. Find the velocity of the particle at times t=a, t=1, t=2, t=3
Thanks!

Explanation / Answer

1)

o F'(2) will be your slope, m, in y=mx+b

F'(x)= [5(1+x^2) - 5x(2x)]/[1+x^2]^2 (quotient rule)

so F'(2)= [5(5)-10(4)]/(25) = -15/25 = -3/5

solve for y-int, given (x,y) --> (2,2)

2 = (-3/5)(2) +b
b = 2 +6/5 = 16/5

tangent line = (-3/5)x + 16/5

2)

If you mean f(t)=2t+1/t+3, then it's f'(t)=2-1/t

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.