document.write( "Question 1003949: differentiate the following function
\n" ); document.write( " f(x)= e^((x^3+2x)) \n" ); document.write( "

Algebra.Com's Answer #620551 by rothauserc(4718) $\"\"$ $\"About$

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f(x)= e^((x^3+2x))
\n" ); document.write( "Find the derivative of the following via implicit differentiation:
\n" ); document.write( "d/dx(f(x)) = d/dx(e^(2x+x^3))
\n" ); document.write( "The derivative of f(x) is f'(x)
\n" ); document.write( "f'(x) = d/dx(e^(2x+x^3))
\n" ); document.write( "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
\n" ); document.write( "f'(x) = e^(x^3+2x) * d/dx(2x+x^3)
\n" ); document.write( "Differentiate the sum term by term and factor out constants
\n" ); document.write( "f'(x) = 2 d/dx(x)+d/dx(x^3) * e^(2x+x^3)
\n" ); document.write( "The derivative of x is 1
\n" ); document.write( "f'(x) = e^(2 x+x^3) * (d/dx(x^3)+1*2)
\n" ); document.write( "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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\n" ); document.write( "f'(x) = e^(2 x+x^3) (2 + 3x^2)
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