# What is the derivative of #(4x^8-sqrt(x))/(8x^4)#?

To begin, rewrite your function as follows:

This could be rephrased as

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

To find the derivative of the function ((4x^8 - \sqrt{x})/(8x^4)), we can use the quotient rule. The quotient rule states that if (u(x)) and (v(x)) are differentiable functions, then the derivative of their quotient is ((u'v - uv')/(v^2)). Applying the quotient rule to the given function, we have:

[ f(x) = \frac{4x^8 - \sqrt{x}}{8x^4} ]

where (u(x) = 4x^8 - \sqrt{x}) and (v(x) = 8x^4). Now, differentiate (u(x)) and (v(x)) with respect to (x):

[ u'(x) = 32x^7 - \frac{1}{2\sqrt{x}} ]

[ v'(x) = 32x^3 ]

Now, apply the quotient rule:

[ f'(x) = \frac{(32x^7 - \frac{1}{2\sqrt{x}})(8x^4) - (4x^8 - \sqrt{x})(32x^3)}{(8x^4)^2} ]

Simplify this expression to get the derivative of the given function.

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 implicitly differentiate #2=e^(xy)cosxy #?
- How do you derive #y = (4x^4 − 2) / (-x^2 + 1)# using the quotient rule?
- How do you find the derivative of #f(x)= (x-1/x+1)^3# using the chain rule?
- How do you differentiate #x^pi#?
- How do you use implicit differentiation to find dy/dx given #x^3+3x^2y+y^3=8#?

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