Differentiate 4*(8-3x)^3
12(8-3x)^2 (-3)
= -36(8-3x)^2
To differentiate the expression 4*(8-3x)^3, we can use the chain rule and the power rule of differentiation. The chain rule states that if we have a function of a function, the derivative is the derivative of the outer function times the derivative of the inner function. The power rule states that if we have an expression of the form (ax^n), the derivative is (n * ax^(n-1)).
Let's break down the steps to differentiate 4*(8-3x)^3:
Step 1: Apply the power rule to the expression inside the parentheses: (8-3x)^3. The derivative of (8-3x) will be -3. The exponent decreases by 1, so we'll have (8-3x)^(3-1), which simplifies to (8-3x)^2.
Step 2: Multiply the result from step 1 by the derivative of the expression inside the parentheses. The derivative of (8-3x)^2 is 2*(8-3x)^(2-1), which simplifies to 2*(8-3x).
Step 3: Multiply the entire expression by the derivative of the coefficient 4. The derivative of a constant (4 in this case) is zero.
Putting it all together, the derivative of 4*(8-3x)^3 is:
4 * 2*(8-3x) * (8-3x)^2
Simplifying further, we get:
8 * (8-3x) * (8-3x)^2
= 8*(8-3x)^3