Differentiate the following function. (7x-5)(3x+9)
To differentiate the function (7x - 5)(3x + 9), we can use the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product, u(x)v(x), is given by:
d/dx [u(x)v(x)] = u'(x)v(x) + u(x)v'(x)
Let's apply the product rule to differentiate the given function:
u(x) = 7x - 5
v(x) = 3x + 9
First, let's find the derivatives of u(x) and v(x):
u'(x) = d/dx[7x - 5] = 7
v'(x) = d/dx[3x + 9] = 3
Now, substituting these values into the product rule formula:
d/dx [(7x - 5)(3x + 9)] = (7)(3x + 9) + (7x - 5)(3)
Expanding and simplifying this expression, we get:
= 21x + 63 + 21x - 15
Combining like terms, we have:
= 42x + 48
Therefore, the derivative of the function (7x - 5)(3x + 9) is 42x + 48.