i tried to find the derivative of this questions but it was way too hard, and i got it wrong on a test.. i need help
y=x4/3 - (sqr.root)5x + 4/x
do you mean
x^(4/3) - (5x)^.5 + 4 x^-1 ??
if so then
(4/3)x^(1/3) - .5(5x)^-.5 - 4x^-2
yah that is what i mean except for the first part of the questions is actually x^4/3 .. sorry lol
and i understand that part but is the derivative of x^4/3 = x^(1/12)?
oh and i just realized that looks like something different .. the first variable is x^4(divided by)3
d/dx [ (1/3) x^4 ] = (1/3)(4) x^3
= (4/3) x^3
(3x-4)^5 x(sqaure root)9x^2+4
Sure, I can help you find the derivative of the given equation. First, let's break down the equation into smaller parts to make it easier to differentiate.
y = x^(4/3) - √(5x) + 4/x
To find the derivative, you will need to apply the rules of differentiation. Here are the steps to find the derivative:
Step 1: Differentiate each term separately.
For the first term, y = x^(4/3), we can use the power rule. The power rule states that if we have a function f(x) = x^n, then its derivative is f'(x) = n * x^(n-1). So applying this rule, we differentiate the first term as follows:
d/dx (x^(4/3)) = (4/3) * x^(4/3 - 1) = (4/3) * x^(1/3)
Next, for the second term, y = √(5x), we can use the chain rule. The chain rule states that if we have a composite function f(g(x)), then its derivative is given by f'(g(x)) * g'(x). The function inside the square root is g(x) = 5x, and f(g) = √(g). Applying the chain rule, we differentiate the second term as follows:
d/dx (√(5x)) = (1/2) * (5x)^(-1/2) * 5
Simplifying further, we get:
= (1/2) * 5 * (5x)^(-1/2)
= 5/2 * (5x)^(-1/2)
= 5/2 * (1/√(5x))
Finally, for the third term, y = 4/x, we can once again use the power rule:
d/dx (4/x) = -4/x^2
Step 2: Combine the derivatives of each term to find the final derivative.
Now that we have differentiated each term, we can combine them to find the derivative of the entire equation. So the final derivative, dy/dx, is:
dy/dx = (4/3) * x^(1/3) + 5/2 * (1/√(5x)) - 4/x^2
So, the derivative of the given equation is (4/3) * x^(1/3) + 5/2 * (1/√(5x)) - 4/x^2.
Remember that differentiating an equation involves multiple steps and applying various rules. It's important to practice and understand these rules to be able to tackle more complex equations.