How do you find #f'(4)# if #f(x)=2sqrt(2x)#?
By signing up, you agree to our Terms of Service and Privacy Policy
To find ( f'(4) ) if ( f(x) = 2\sqrt{2x} ), you first need to find the derivative of ( f(x) ) with respect to ( x ), denoted as ( f'(x) ). Then, substitute ( x = 4 ) into the derivative function ( f'(x) ).
Using the power rule and chain rule, the derivative of ( f(x) = 2\sqrt{2x} ) with respect to ( x ) is:
[ f'(x) = \frac{d}{dx} [2\sqrt{2x}] = 2 \cdot \frac{1}{2\sqrt{2x}} \cdot \frac{d}{dx} [2x] = \frac{1}{\sqrt{2x}} \cdot 2 = \frac{2}{\sqrt{2x}} ]
Now, substitute ( x = 4 ) into ( f'(x) ):
[ f'(4) = \frac{2}{\sqrt{2 \cdot 4}} = \frac{2}{\sqrt{8}} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}} ]
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.
- What is the equation of the line tangent to # f(x)=sinpi/x # at # x=1 #?
- How does (x-y)(x^2+xy+y^2)=x^3-y^3 help to prove that derivative of x^(1/3) is 1/(3x^(2/3)) ?
- What is the equation of the tangent line of #f(x) =(sin2x)/(cos2x)-tanx# at #x=pi/8#?
- How do you find the equation of a line tangent to the function #y=x^3-3x^2+2# at (3,2)?
- What is the equation of the tangent line of #f(x)=x^2-lnx^2/(x^2+9x)-1# at #x=-1#?

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