I'm not sure how to derive these: y = log(2)x^(1/3) (2)=base and y = √x(e^3x²)
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Originally Posted by b521 I'm not sure how to derive these: y = log(2)x^(1/3) (2)=base and y = √x(e^3x²) To your first question: Rewrite the given equation: You only have to know how is differentiated, all other factors are constant. Do the second question similarly.
Only ln(x) is differentiated? So it would be 1/3xln2 ?
Well, with parentheses to make it clearer: 1/(3(ln 2)x). Yes, that is correct. In general, the derivative of is while the derivative of with a any positive number, is . The derivative of is while the derivative of with a any positive number is .
So for the second equation, would the answer use fg'+gf'? 6ln(3x²)x^(1/2) + 1/(2x^(1/2))e^(3x²) (6√x)ln(3x²) + e^(3x²)/(2√x) Is this answer correct?
Originally Posted by b521 So for the second equation, would the answer use fg'+gf'? 6ln(3x²)x^(1/2) + 1/(2x^(1/2))e^(3x²) (6√x)ln(3x²) + e^(3x²)/(2√x) Is this answer correct? 1. I assume that the given function reads: 2. Re-write so that you have only one power to the base e at the RHS: 3. Now differentiate using the chain rule: Simplify! 4. If you want to use the product rule and the chain rule you'll get: Simplify!
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