# How do you find the derivative of #f(x)=root5(x)#?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of (f(x) = \sqrt{5x}), you can use the power rule for differentiation.

The power rule states that if you have a function of the form (g(x) = x^n), then its derivative is (g'(x) = nx^{n-1}).

In this case, you can rewrite (f(x)) as (f(x) = 5x^{1/2}). Applying the power rule, the derivative of (f(x)) is:

[f'(x) = \frac{1}{2} \cdot 5x^{1/2 - 1}] [f'(x) = \frac{5}{2}x^{-1/2}] [f'(x) = \frac{5}{2\sqrt{x}}]

So, the derivative of (f(x) = \sqrt{5x}) is (f'(x) = \frac{5}{2\sqrt{x}}).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you differentiate #f(x)=x*e^(1-sqrt(x)*ln(x))#?
- How do you differentiate # y=sec (3x^2 - x)# using the chain rule?
- How do you use the chain rule to differentiate #y=(x^2+5x)^2+2(x^3-5x)^3#?
- How do you differentiate #g(x) =e^x (x^3 + 4) # using the product rule?
- How do you differentiate #f(x)=(sec^5 (1/x))^(1/3)# using the chain rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7