Question

Find y' if the equation
y=x⁵Inx​

Answer 1

Answer:

y' = x⁴(5ln(x) + 1)

Step-by-step explanation:

y = x⁵ln(x)

y' = (x⁵ln(x))'

y' = (x⁵)'.ln(x) + (ln(x))'.x⁵

y' = 5x⁴.ln(x) + (1/x)x⁵

y' = 5x⁴ln(x) + x⁴

y' = x⁴(5ln(x) + 1)

Answer 2

Answer:

Area of triangle =

2

1

[x

1

(y

2

−y

1

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

3

)]

=

2

1

[x(7−5)+5(5−y)−4(4−7)]

Given A,B and C are collinear, then area of triangle must be zero.

∴

2

1

[x(7−5)+5(5−y)−4(4−7)]=0

⇒

2

1

[2x−25+5y−4y+25]=0

⇒

2

1

(2x+y+3)=0

Then, relation between x and y is 2x+y+3=0