nobody
1. suppose that f(x) and g(x) are twise differentiable at x=a,
show that
(fg)"(a)= f(a) g"(a) + 2f'(a) g'(a) + f"(a) g(a)
__________________________________________________ _____________
2. Use the definition of derivative to show that for the function
f(x)=3(x)^(1/3)
(f of x is equal to 3 x to the power 1/3)
we have f'(a)=a^(2/3), for every "a" belongs to "R" (Set of real numbers)
[Use the identity (a^3)-(b^3)= (a-b)((a^2)+ab+(b^2))]
__________________________________________________ _____________
3. Differentiate the following and prove the necessary expressions as given
a) If y=xtanx
show that
x sin²x (dy/dx)=x²tan²x +y sin²x
_____
b) y= (x+√ x²-1 )ⁿ
prove that
(x²-1) (dy/dx)²=n²y²
Plz help me to solve these.
Use the product rule- twice.
Okay, what did you get for dy/dx?__________________________________________________ _____________
2. Use the definition of derivative to show that for the function
f(x)=3(x)^(1/3)
(f of x is equal to 3 x to the power 1/3)
we have f'(a)=a^(2/3), for every "a" belongs to "R" (Set of real numbers)
[Use the identity (a^3)-(b^3)= (a-b)((a^2)+ab+(b^2))]
__________________________________________________ _____________
3. Differentiate the following and prove the necessary expressions as given
a) If y=xtanx
show that
x sin²x (dy/dx)=x²tan²x +y sin²x
_____
Again, what did you get for dy/dx?b) y= (x+√ x²-1 )ⁿ
prove that
(x²-1) (dy/dx)²=n²y²
Plz help me to solve these.