Let the function f(x) have the property that f′(x)=(x+1)/(x−3). If g(x)=f(x^2) find g′(x)

1 answer:

3 0

Solve this using chain rule:
Start with g(x) = f(x^2), Differentiate both sides:
$g'(x) = f'(x^2) * (x^2)' \\ \\ g'(x) = 2x f'(x^2)$

Now sub in "x^2" into given f'(x) function:
$g'(x) = 2x*\frac{ x^2 +1}{x^2 -3}$

You might be interested in

A triangle's area is given by the expression 3x2-x+12. The height is 6x. The base off the triangle is the quotient of the area a

patriot [66]

You have known the formula Length of base is la division of Area and a haft of the height.
So we have 3
$(3 {x}^{2} - x + 12) \div ( \frac{1}{2} \times 6x)$
or
$(3 {x}^{2} - x + 12) \div 3x$
$3 {x}^{2} \div 3x +( - x \div 3x) + 12 \div 3x$
and
$x - \frac{1}{3} + \frac{4}{x}$
have fun

6 0

2 years ago

Determine the intercepts of the line that correspond to the following table of values.

Dahasolnce [82]

We know that
to find the equation of a line i need two points

let
point A-----> (-21,10)
point B-----> (-28,14)

step 1
find the slope m
m=(y2-y1)/(x2-x1)-----> m=(14-10)/(-28+21)----> m=-4/7

step 2
find the equation of a line with
m=-4/7 and the point A (-21,10)
y-y1=m*(x-x1)------> y-10=(-4/7)*(x+21)---> y=(-4/7)x-12+10
y=(-4/7)x-2

step 3
find x intercept
for y=0
y=(-4/7)x-2------> 0=(-4/7)x-2-----> 4/7x=-2----> x=-14/4----> x=-3.5

the x intercept is (-3.5,0)

step 4
find the y intercept
for x=0
y=(-4/7)x-2--------> y=-2
the y intercept is (0,-2)

the answers are
the x intercept is (-3.5,0)
the y intercept is (0,-2)

see the attached figure