Let z = √(x^2 +2x +4).
Then your expression becomes
y = (z^2)^z
y = z^(2z)
And the derivative with respect to x is
y' = z^(2z)*(2z' +2ln(z)z')
= (2z')(1 +ln(z))(z^(2z))
Now
z' = (2x +2)/(2√(x^2 +2x +4)
= (x +1)/√(x^2 +2x +4)
So, your derivative is
y' = 2(x +1)/√(x^2 +2x +4) * (1 + (1/2)ln(x^2 +2x +4)) * (x^2 +2x +4)^√(x^2 +2x +4)
For x = 0, this becomes
2(1)/√4 * (1 +(1/2)ln(4)) * 4^√4
= 16*(1 + ln(2))
Answer:
6x+3(1.25)=6.90 or 6x+ 3.75=6.90
Step-by-step explanation:
Use pythagora's theorem to test if it is a right triangle
c^2 = a^2 + b^2
65^2 = 52^2 + 43^2
4225 = 2704 + 1849
4225 =/= 4553
therefore it is not a right triangle as it does not comply to pythagora's theorem
Answer:
r=13
d=26
Step-by-step explanation:
circumference=26π
C=2πr
r=C/2π
r=26π/2π
r=13
d=2r=2(13)=26
