How do you differentiate #f(x)= 7xsinx# using the product rule?
According to the product rule:
Adding this in place of the product rule:
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate the function ( f(x) = 7x \sin(x) ) using the product rule:
Let ( u(x) = 7x ) and ( v(x) = \sin(x) ).
Using the product rule, the derivative of ( f(x) ) with respect to ( x ) is:
[ f'(x) = u(x)v'(x) + v(x)u'(x) ]
where ( u'(x) ) and ( v'(x) ) are the derivatives of ( u(x) ) and ( v(x) ) respectively.
First, find ( u'(x) ) and ( v'(x) ):
( u'(x) = 7 ) (derivative of ( 7x ) with respect to ( x ))
( v'(x) = \cos(x) ) (derivative of ( \sin(x) ) with respect to ( x ))
Now, plug these into the product rule formula:
[ f'(x) = (7x)(\cos(x)) + (\sin(x))(7) ]
So, the derivative of ( f(x) ) with respect to ( x ) is:
[ f'(x) = 7x\cos(x) + 7\sin(x) ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7