Question

determine the equation of tangent line to the graph of
y=tan(1/2x)+xcot(2x+pi/4) at x=pi/2

Answer #1

Suppose that f(x) = (2x)/((4-2x)^3)
Find an equation for the tangent line to the graph of f at
x=1.
Tangent line: y =

f(x)=1/2x ln x^4, (-1,0)
a) find an equation of the tangent line to the graph of the
function at the indicated point.
b) Use a graphing utility to graph the function and its tangent
line at the point.

1.) Find the equation of the tangent line to the graph of the
function f(x)=5x-4/2x+2 at the point where x=2
2.) Find the derivative: r(t)=(ln(t^3+1))^2

Use implicit differentiation to find an equation of the line
tangent to the curve sin(x+y)=2x-y at the point (pi,2\pi )

Find the equation of the tangent line to y= cos x at x= pi/2

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

1.Given that y = x + tan−1 y , find dy dx
2.Determine the equation of the tangent line to the curve y = (2
+ x) e −x at the point (0, 2)

Find the equation of the tangent line to the graph of y = e x
2−1 at the point (1, 1)

Use implicit differentiation to find an equation of the line
tangent to the curve sin(x+y)=2x-y at the point (pi, 2pi )

Write the equation of the tangent line to the graph of y = (x^2
− 16x)/(4x − x^3) at x = 4. Check the reasonableness of your answer
by graphing both the function and the tangent line

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