I need to find the derivative and can't do them when they are raised to powers? Thank You.
m(x)x^5 - 5x^3+7x -4)^10 (4x^9 +19)^23 this on is tuff!
Your brackets don't match , also there is no equal sign
is it ...
m(x) = (x^5 - 5x^3 + 7x - 4)^10 * (4x^9 + 19)^23 ??
(the * means multiplication)
the key, however, is the chain rule. If
f = u^n, then
df/dx = nu^n-1 * du/dx
It's just the familiar power rule, but you have to multiply by the derivative of what's raised to the power.
For example, if you have
f(x) = (3x^2-4x+5)^5, then
let u = 3x^2 - 4x + 5.
Then all you have is
f(x) = u^5
df/dx = 5u^4 du/dx
But that's easy, because du/dx = 6x-4, so the final answer is
df/dx = 5(3x^2-4x+5)^4 (6x-4)
To find the derivative of a function that involves powers, such as in your case, we can use the chain rule. The chain rule states that if we have a composition of functions, then we can find the derivative by taking the derivative of the outer function multiplied by the derivative of the inner function.
In your expression, we have two terms raised to powers: (m(x)x^5 - 5x^3+7x -4)^10 and (4x^9 +19)^23. Let's tackle these separately.
First, let's focus on (m(x)x^5 - 5x^3+7x -4)^10:
1. Identify the inner function: m(x)x^5 - 5x^3+7x -4
2. Take the derivative of the inner function (using the power rule, product rule, and sum rule as necessary).
3. Multiply the derivative from step 2 by the power of the outer function (10 in this case).
Now, let's move on to (4x^9 +19)^23:
1. Identify the inner function: 4x^9 +19
2. Take the derivative of the inner function (again, using the power rule).
3. Multiply the derivative from step 2 by the power of the outer function (23 in this case).
After finding the derivatives of both terms, you can multiply them together to get the final derivative of the entire expression.
Remember that it may get quite complex due to the high powers, so it's essential to double-check your calculations and simplify the final result if possible.