Nope. You need to use the chain rule. It will help to write your function asCrossFit415 said:I'm on mobile so I can't use latex.
Differentiate:
g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains.
So I got the derivative which is,
g'(x)=(-4x^3) ^1/2
CrossFit415 said:What should I do with the -+√2 ?
I don't know what to do next
NO. Do it again and show each step.CrossFit415 said:I have
G'(x) = 1/2(4-x)^-1/2 • -4x^3
The domain will be the intersection of the natural domain of the derivative (not what you have above) and the given domain of the function, [itex][-\sqrt{2}, \sqrt{2}][/itex].Then how would I determine the domains? I know 4-x^4 >= 0. So what about the two square roots?
What should I do with the +/-√2 ?
HallsofIvy said:Please do NOT use "x" both as the variable and for multiplication!
Much better.CrossFit415 said:g'(x) = 1/2(4-x^4)^1/2-1 • d/dx (4-x^4)
= 1/2(4-x^4)^-1/2 • -4x^3
Should I keep continuing?
Then
= -2x^3(4-x^4)^-1/2
Mark44 said:Much better.
When you write expressions on a single line, you need to use more parentheses. The above should be written as -2x^3(4-x^4)^(-1/2).
Your question was answered twice in this thread.CrossFit415 said:So should I just plug in +/- √2 for x to find the domains? Or leave it alone? Are the domains just +/- √2 ?
The differentiation problem for a square root function involves finding the derivative of the square root function. This means finding the rate of change of the function at any given point on its graph.
To differentiate a square root function, you can use the power rule, where n is the power of the function. For a square root function, n=1/2, so the derivative of the function is equal to 1/2 times the original function raised to the power of -1/2.
The domain of a square root function is all real numbers greater than or equal to 0, as the square root of a negative number is undefined. The range is also all real numbers greater than or equal to 0, as the square root of any number will always be a positive value.
The graph of a square root function will change from a curve to a straight line as you differentiate it. The slope of the line at any point on the graph will be equal to the derivative of the function at that point.
Differentiating a square root function can be used to find the instantaneous rate of change in situations where the dependent variable is related to the independent variable by a square root function. This can be useful in fields such as physics, engineering, and economics.