To differentiate -7xy³, we can differentiate each term separately using the power rule.
The power rule states that if we have a term of the form cx^n, where c is a constant and n is a variable with a constant coefficient, we can differentiate it by multiplying the coefficient by the exponent and then subtracting 1 from the exponent.
Let's differentiate each term separately:
Differentiating -7:
The constant -7 does not have any variables, so its derivative is 0.
Differentiating x:
The variable x has an exponent of 1, so its derivative is 1.
Differentiating y³:
The variable y has an exponent of 3, so its derivative is 3y^2.
Putting it all together, the derivative of -7xy³ is:
0x + 1(-7)y³ + (-7x)3y²
Simplifying this expression, we get:
-7y³ - 21xy²
Therefore, the derivative of -7xy³ is -7y³ - 21xy².