Differentiation question - someone please help!?

Question

A curve C represents the graph of y=(x^2)/25 x≥0

The points A and B on the curve C have x-coordinates 5 and 10 respectively.
a)Write down the y-coordinates of A and B
b) Find an equation of the tangent to C at A

I can do part a), but i don't get how i can differentiate (x^2)/25?????!!!!!

Thank YOU in advance :D

Answer 1

x^2/25

Differentiating x^2/25, we get
2x/25

Answer 2

Part a)
f(x) = x² / 25
f(5) = 25/25 = 1-------->A (5,5)
f(10) = 100 / 25 = 4--->B (10,4)

Part b)
f `(x) = 2x / 25
f `(5) = 10 / 25 = 2 / 5
m = 2 / 5
A (5,1)
y - 1 = (2/5) (x - 5)
y = (2/5) x - 2 + 1
y = (2/5) x - 1

Answer 3

to differentiate, you take the power in front of the number, then subtract the power by 1.
derivative: 2x/25

for the question b: i think the equation will be 2x-5y = 5

Answer 4

The answer for differential is correct 2x/25 to find the slope of the tangent at point A, simply substitute the independent variable value for Ax for x.

The slope of the tangent is 2A/25

Answer 5

y'=[(x^2)/25]'=(x^2)'/25=2x/25
Τhe tangent to C at A (x=5):
y'=2*5/25=2/5=0.4

Answer 6

d/dx( x^2 /25)

= 1/25 * 2x

=( 2x) /25

now subs the values of (x,y) to get the equation of tangent