You can put this solution on YOUR website! f(x)= e^((x^3+2x))
Find the derivative of the following via implicit differentiation:
d/dx(f(x)) = d/dx(e^(2x+x^3))
The derivative of f(x) is f'(x)
f'(x) = d/dx(e^(2x+x^3))
Using the chain rule, d/dx(e^(x^3+2x)) = ( de^u)/(du) * (du)/( dx), where u = x^3+2x and ( d)/( du)(e^u) = e^u
f'(x) = e^(x^3+2x) * d/dx(2x+x^3)
Differentiate the sum term by term and factor out constants
f'(x) = 2 d/dx(x)+d/dx(x^3) * e^(2x+x^3)
The derivative of x is 1
f'(x) = e^(2 x+x^3) * (d/dx(x^3)+1*2)
Use the power rule, d/dx(x^n) = n * x^(n-1), where n = 3: d/dx(x^3) = 3 * x^2
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f'(x) = e^(2 x+x^3) (2 + 3x^2)
The rule (in words) for taking the derivative of
e raised to a power:
1. Copy the expression over.
2. Multiply by the derivative of the exponent.
Edwin
