Find the Derivative of the Product y = 5x²sinx
| August 12, 2021 | education
To calculate the derivative in this case, we use the formula for the derivative of the product (uv) ‘= u’ * v + u * v ‘, where u = 5×2, v = sinx:
y ‘= (5x ^ 2)’ * sinx + 5x ^ 2 * (sinx) ‘.
Now we apply the formula for the derivative of the power function and the derivative of the sine from the table of derivatives and find:
y ‘= 2 * 5x * sinx + 5x ^ 2 * cosx = 10xsinx + 5x2cosx = 5x (2sinx + xcosx).
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
