I am having trouble with this problem also
derivative
differentiate
f(x)=(3-x)^4(x+5)^3
so far I have 4(3-x(x+5)^3+3(x+5)(3-x)
Not quite right.
Treat it as d/dx[u(x) + v(x)]
= u dv/dx + v du/dx
u(x) = (3-x)^4 v(x) = (x+5)^3
du/dx = -4(3-x))^3 (using the chain rule)
dv/dx = 3(x+5)^2
[4(3-x)^3*(-1)(x+5)^3] + [3(x+5)^2*(3-x)^4]
To find the derivative of the function f(x) = (3-x)^4(x+5)^3, you can use the product rule of differentiation.
The product rule states that if you have two functions u(x) and v(x), the derivative of their product is given by:
d/dx[u(x) * v(x)] = u(x) * dv/dx + v(x) * du/dx
In this case, let's let u(x) = (3-x)^4 and v(x) = (x+5)^3.
Now, we need to find du/dx and dv/dx.
To find du/dx, we can use the chain rule. First, differentiate (3-x)^4 with respect to the inner function (3-x), then multiply by the derivative of (3-x) with respect to x.
du/dx = d/d(3-x) [(3-x)^4] * d(3-x)/dx
= 4(3-x)^3 * -1
= -4(3-x)^3
To find dv/dx, we can simply differentiate (x+5)^3 with respect to x.
dv/dx = d/dx[(x+5)^3]
= 3(x+5)^2
Now, we can substitute these values into the product rule formula:
d/dx[(3-x)^4(x+5)^3] = (3-x)^4 * dv/dx + (x+5)^3 * du/dx
Substituting in the values, we get:
d/dx[(3-x)^4(x+5)^3] = (3-x)^4 * (3(x+5)^2) + (x+5)^3 * (-4(3-x)^3)
Simplifying this expression will give you the correct derivative of the function.