Home > Calculus > Tangent Line to a Curve

How do you find the slope of the line tangent to the graph of #y = x ln x# at the point ( 1,0 )?

Answer 1

Christopher Allers

# y = x-1 #

The slope of the tangent at any particular point is given by the derivative.

We have #y=xlnx#

Differentiating wrt #x# using the product rule gives us:

# dy/dx=(x)(d/dxlnx) + (d/dxx)(lnx) #
# :. dy/dx=(x)(1/x) + (1)(lnx) #
# :. dy/dx=1 + lnx #

So, At# (1.0), dy/dx=1+ln1=1 #

So the required tangent passes through #(1.0)# and has slope #1#
Using #y-y_1=m(x-x_1)# the required equation is;
# y - 0 = 1(x-1) #
# :. y = x-1 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isabella Ackerman

To find the slope of the line tangent to the graph of y = x ln x at the point (1,0), we can use the derivative of the function. The derivative of y = x ln x can be found using the product rule and the chain rule. Taking the derivative, we get:

dy/dx = ln x + 1

To find the slope at the point (1,0), we substitute x = 1 into the derivative:

dy/dx = ln 1 + 1 = 0 + 1 = 1

Therefore, the slope of the line tangent to the graph of y = x ln x at the point (1,0) is 1.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.