How do you differentiate #f(x)=(2x^24x+4)e^x# using the product rule?
When combined with other accepted differentiation rules, this rule produces
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(x) = (2x^2  4x + 4)e^x ) using the product rule, follow these steps:

Identify the functions ( u(x) ) and ( v(x) ): ( u(x) = 2x^2  4x + 4 ) ( v(x) = e^x )

Differentiate ( u(x) ) and ( v(x) ) separately: ( u'(x) = 4x  4 ) ( v'(x) = e^x )

Apply the product rule: ( f'(x) = u'(x)v(x) + u(x)v'(x) ) ( f'(x) = (4x  4)e^x + (2x^2  4x + 4)e^x )

Simplify the expression: ( f'(x) = (4x  4 + 2x^2  4x + 4)e^x ) ( f'(x) = (2x^2  4)e^x )
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 How do you differentiate #f(x) = (x^3+cos3x)^(1/2)?# using the chain rule?
 How do you differentiate #f(x)=(14x)/(1+4x)# using the quotient rule?
 If #f(x) =e^(2x1) # and #g(x) = 5sin^2x^2 #, what is #f'(g(x)) #?
 How do you implicitly differentiate #y= y(xy)^2 + e^(x y) #?
 How do you find the derivative of #h(x) = (2x^23x+1)/x#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7