Differentiate (4x+2)³ with respect to x hence find the value of dy/dx when x=1
To differentiate (4x+2)³ with respect to x, you can use the chain rule.
Let u = 4x+2.
Now, rewrite the given expression as u³.
(d/dx)(u³) = (d/du)(u³) * (du/dx)
The derivative of u³ with respect to u is 3u².
The derivative of u = 4x+2 with respect to x is 4.
Therefore, dy/dx = 3u² * 4.
Substituting u = 4x+2 back into the expression, we have:
dy/dx = 3(4x+2)² * 4
When x = 1:
dy/dx = 3(4(1)+2)² * 4
= 3(6)² * 4
= 3(36) * 4
= 108 * 4
= 432
To differentiate (4x+2)³ with respect to x, we can use the chain rule.
The chain rule states that if we have a function g(f(x)), the derivative of g(f(x)) with respect to x is given by g'(f(x)) multiplied by f'(x).
Let's step-by-step differentiate (4x+2)³ using the chain rule:
Step 1: Identify the inner function and the outer function.
In this case, the inner function is 4x+2, and the outer function is ( )³.
Step 2: Compute the derivatives of the inner and outer functions.
The derivative of the inner function 4x+2 is simply 4.
The derivative of the outer function ( )³ is 3( )².
Step 3: Apply the chain rule.
The derivative of (4x+2)³ with respect to x is given by the derivative of the outer function multiplied by the derivative of the inner function.
So, dy/dx = 3(4x+2)² * 4
Simplifying further, dy/dx = 12(4x+2)²
To find the value of dy/dx when x=1, substitute x=1 into the expression above:
dy/dx = 12(4(1)+2)²
= 12(6)²
= 12 * 36
= 432
Therefore, when x=1, dy/dx is equal to 432.