Differentiate following with respect to x.
(3x2 – 5ax + a2)4
I will assume that you have exponents, and it is ...
y = (3x^2 - 5ax + a^2)^4 , where a is a constant
dy/dx = 4(3x^2 - 5ax + a^2)^3 (6x - 5a)
= 4(6x-5a)(3x^2 - 5ax + a^2)^3
let me know if a is NOT a constant.
To differentiate the given expression (3x^2 - 5ax + a^2)^4 with respect to x, we can use the chain rule.
Step 1: Write down the expression.
f(x) = (3x^2 - 5ax + a^2)^4
Step 2: Apply the chain rule.
The chain rule states that if you have a function of a function (in this case, f(g(x))), then the derivative is given by the derivative of the outer function multiplied by the derivative of the inner function.
In this case, the outer function is f(x) = u^4 and the inner function is g(x) = 3x^2 - 5ax + a^2.
So, we have:
f'(x) = (4u^3) * g'(x)
Step 3: Find the derivative of the inner function, g'(x).
To find g'(x), we need to find the derivative of each term separately.
The derivative of 3x^2 is 6x.
The derivative of -5ax is -5a.
The derivative of a^2 is 0 (since a^2 is a constant with respect to x).
So, g'(x) = 6x - 5a.
Step 4: Substitute the values back into the chain rule formula.
f'(x) = (4u^3) * g'(x)
= (4(3x^2 - 5ax + a^2)^3) * (6x - 5a)
Therefore, the derivative of the expression (3x^2 - 5ax + a^2)^4 with respect to x is:
f'(x) = (4(3x^2 - 5ax + a^2)^3) * (6x - 5a)