Answer:
dy/dx = (1 / x^3 + x) × (3x² + 1) × (1/2)
Step-by-step explanation:
y = log[ x² × √(x² + 1) ]
y = log[ √(x(x² + 1)) ]
y = log[ √(x^3 + x) ]
y = log[ √(x^3 + x) ]
Now, let a = √(x^3 + x)
Then y = log(a)
Find dy/da.
y = log(a)
dy/da = (1 / a)
dy/da = (1 / √(x^3 + x))
Find da/dx using chain rule.
a = √(x^3 + x)
Let b = x^3 + x, then a = √b
da/dx = (db / dx) × (da / db)
da/dx = (3x² + 1) × (1/2)× (b)^(-1/2)
da/dx = (3x² + 1) × (1/2)× (x^3 + x)^(-1/2)
Finally, find dy/dx using chain rule.
dy/dx = (dy/da) × (da/dx)
dy/dx = (1 / √(x^3 + x)) × (3x² + 1) × (1/2)×
(x^3 + x)^(-1/2)
dy/dx = (1 / (x^3 + x)) × (3x² + 1) × (1/2)
Answer:
| 5x| = 0
Step-by-step explanation:
Absolute values have two solutions, one positive and one negative
The exception to this rule is when it is equal to zero
+0 = -0 = 0
5x = 0
x =0
Answer:
3√2
Step-by-step explanation:
If you draw the diagonal, you have a 45°45°90° triangle.
The two legs are 3, so the hypotenuse is 3√2
2x³+18x²<span>-18x-162 =
2(</span>x³+9x²-9x-81)=
2(x²(x+9)-9(x+9))=
2(x²-9)(x+9)=
2(x+3)(x-3)(x+9)
Answer: k=3
