# How do you differentiate #(3x-4/x)^2 (1-x+7x^2)^4#?

#2(3x - 4/x^2) (3 + 4/x^2)[(1 - x + 7 x^2)^4] +(3x - 4/x^2)^2[4(1 - x + 7 x^2)^3(-1 + 14x)#

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

To differentiate the expression ((3x - \frac{4}{x})^2 \times (1 - x + 7x^2)^4), you would use the product rule of differentiation. The product rule states that if you have two functions, (u(x)) and (v(x)), then the derivative of their product, (u(x) \times v(x)), is given by (u'(x) \times v(x) + u(x) \times v'(x)), where (u'(x)) and (v'(x)) represent the derivatives of (u(x)) and (v(x)) with respect to (x), respectively. Applying this rule to the given expression, you would differentiate each part separately and then combine the results using the product rule.

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 #g(x) = (x/2)(x-e^(2x))# using the product rule?
- How do you differentiate #f(x)=sqrt((1-xe^(2x))^3# using the chain rule.?
- How do you find the derivative of #x^3(2x-5)^4#?
- How do you differentiate #f(x)=x-x^2e^x-xlnx# using the product rule?
- How do you differentiate #g(y) =e^x(x^2 + 3) # using the product rule?

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