Use the product rule to find the derivative of (2x^2 + 3)(3x + 5).
recall that the derivative of f(x)*g(x) is just
f'(x)*g(x) + f(x)*g'(x)
which means, we first take the derivative of the first function of x (the f(x)) then multiply this by the second function of x (the g(x)) and add this to the product of f(x) and derivative of g(x).
from the problem,
let f(x) = (2x^2 + 3)
let g(x) = (3x + 5)
thus
f'(x) = 4x
g'(x) = 3
and therefore,
f'(x)*g(x) + f(x)*g'(x)
(4x)(3x+5) + (2x^2 + 3)(3)
12x^2 + 20x + 6x^2 + 9
18x^2 + 20x + 9
hope this helps~ :)
Duplicate post.
See also
http://www.jiskha.com/display.cgi?id=1303800740
To find the derivative of the given expression (2x^2 + 3)(3x + 5) using the product rule, you need to follow these steps:
Step 1: Identify the two functions that are being multiplied together.
In this case, the two functions are 2x^2 + 3 and 3x + 5.
Step 2: Apply the product rule formula - (f * g)' = f' * g + f * g', where f' represents the derivative of f and g' represents the derivative of g.
Let's denote the first function as f(x) = 2x^2 + 3 and the second function as g(x) = 3x + 5.
Step 3: Compute the derivatives of both functions f(x) and g(x).
The derivative of f(x) can be found by applying the power rule: f'(x) = 2 * 2x^(2-1) = 4x.
Similarly, the derivative of g(x) can be found as g'(x) = 3.
Step 4: Substitute the derivatives of f(x) and g(x) into the product rule formula.
(f * g)' = f' * g + f * g'
Substituting the derivatives into the formula, we get:
(2x^2 + 3)(3) + (4x)(3x + 5)
Step 5: Simplify and combine like terms.
Expanding and simplifying the expression:
6x^2 + 9 + 12x^2 + 20x
Combining like terms, we have:
18x^2 + 20x + 9
So, the derivative of (2x^2 + 3)(3x + 5) is 18x^2 + 20x + 9.