# How do you use the Product Rule to find the derivative of #(7x^4 + 2x^6) sin(7x)#?

The product rule allows you to differentiate functions that take the form

by using the formula

In your case, you can think of the function as being

This means that you can write

This means that your target derivative will be

By signing up, you agree to our Terms of Service and Privacy Policy

To use the Product Rule to find the derivative of ( (7x^4 + 2x^6) \sin(7x) ), differentiate each term separately, then apply the Product Rule to combine them. The derivative is ( f'(x) = (28x^3 + 12x^5) \sin(7x) + (7x^4 + 2x^6) \cdot 7 \cos(7x) ).

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the slope of the tangent line of #secx-cscy= C #, where C is an arbitrary constant, at #(pi/3,pi/3)#?
- How do you find the derivative of #y=cos 3x#?
- How do you differentiate #f(x) = sqrt(arctan(e^(x-1)) # using the chain rule?
- How do you differentiate #g(x) =e^x*1/x^2# using the product rule?
- How do you differentiate #f(x)=sqrt((1-4x)^3# using the chain rule.?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7