How do you differentiate #f(x)=(2x+3)^4 / x# using the chain rule?
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate the function f(x) = (2x + 3)^4 / x using the chain rule, follow these steps:

Identify the outer function and the inner function. In this case, the outer function is (2x + 3)^4, and the inner function is x.

Differentiate the outer function with respect to the inner function first. The derivative of (2x + 3)^4 with respect to (2x + 3) is 4(2x + 3)^3.

Multiply the result by the derivative of the inner function with respect to x, which is 1.

Then, subtract x times the derivative of the outer function with respect to x. The derivative of (2x + 3)^4 with respect to x is 4(2x + 3)^3 * 2.

Finally, divide the whole expression by x squared.
Putting it all together, the derivative of f(x) is:
(4(2x + 3)^3  8x(2x + 3)^3) / x^2
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 What is the derivative of #e^y cos x = 3 + sin(xy)#?
 If # A = 9/16(4rsin(4r)) # and #(dr)/dt=0.7# when #r=pi/4# then evaluate # (dA)/dt # when #r=pi/4#?
 How do you differentiate #g(x) = cos(5x) (x^24)# using the product rule?
 How do you integrate #f(x)=log_6(2x)/lnx# using the quotient rule?
 How do you differentiate #f(x)= tanx# twice using the quotient rule?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7