The derivative of the function F(x) = cos(x) * sin(5x² + 7) is calculated using the product rule, resulting in the expression -sin(x) * sin(5x² + 7) + (10x) * cos(x) * cos(5x² + 7). The discussion emphasizes the application of the product rule along with the chain rule and power rule for differentiation. Simplification of the resulting expression is deemed minimal, as no further reduction is necessary or possible.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for examples of applying the product and chain rules in trigonometric contexts.
You also used the product rule.n.a.s.h said:Homework Statement
Find the derivative:
F(x)= cos (x)* sin(5x^2 +7)
Homework Equations
The Attempt at a Solution
I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...
= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)
n.a.s.h said:Homework Statement
Find the derivative:
F(x)= cos (x)* sin(5x^2 +7)
Homework Equations
The Attempt at a Solution
I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...
= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)