How do you use the chain rule to differentiate #root3(4x+9)#?
Now differentiate f with respect to p and then p with respect to x, to get differential of f w.r.t x. This is the chain rule. It works out as follows:
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To differentiate √(3(4x + 9)) using the chain rule, first identify the outer function (the square root) and the inner function (3(4x + 9)). Then, differentiate the outer function with respect to the inner function, and multiply the result by the derivative of the inner function.
The derivative of √u, where u is a function of x, is (1/2) * (u^(-1/2)) * du/dx.
For this problem:
Outer function: √u Inner function: 3(4x + 9)
Derivative of the outer function: (1/2) * (u^(-1/2)) * du/dx Derivative of the inner function: d(3(4x + 9))/dx
Now, calculate the derivatives:
Derivative of the outer function: (1/2) * (3(4x + 9))^(-1/2) * d(3(4x + 9))/dx Derivative of the inner function: 12
Finally, multiply the two derivatives:
(1/2) * (3(4x + 9))^(-1/2) * 12
This simplifies to:
6/(√(3(4x + 9)))
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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.
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.
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