Which is the derivative of y = /x3 + 3x - 16/2

Question

 Calculus Question

Answer 1

Basically, take the exponent of each term with a variable, place it in front of the variable as a coefficient, and subtract 1 from the original exponent...

the derivative of    axⁿ = (n)(a)x^n-1

 

Example:   The derivative of 5x³ = 3(5)x^3-1 = 15x²

The derivative of a constant is zero

 

As Muhammad worked out you have:

 

y = √x³ + 3x -16√2

 

Note that roots are fractional exponents...  √x³ =(x³)^1/2 = x ^3/2

 

So you have x^3/2 + 3x - 16√2

 

Take the derivative of each term with a variable... discarding the 16√2 because it is a constant

 

y’ = (3/2)x^{(3/2 -1)} + 3x^1-1 + 0

 

y' = (3/2)x^1/2 + 3x⁰ 

 

Remember that any number to the power of zero = 1 so x⁰=1

 

y' = (3/2)√x + 3

 

This is of course, the same answer Muhammad showed you, but I hope the explanations help.

Answer 2

y= x^3/2 + 3x - 16/2

 

y' = (3/2)x^1/2 +3