WebHere is the derivative of that: y = x^ln x let u = ln x thus, x = e^u thus, du = dx/x thus, y= x^ln x = (e^u)^u = e^ (u²) Let w = u² Thus, dw = 2u du e^ (u²)= e^w Taking the derivative: dy = e^w dw dy = e^ (u²) (2u) (du) dy = (x^ln x) (2 ln x) (dx/x) dy = (2 ln x) x^ [ln (x) - 1)]dx dy/dx = (2 ln x) x^ [ln (x) - 1)] ( 3 votes) peaceumoru WebSimplify e^(3 ln x)

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WebIt is time to simplify the mathematical expression in the right hand side of the equation. d y d x = e x × 3 x 2 + x 3 × e x. In both terms of the right hand side expression of the equation, the natural exponential function in terms of x is commonly appearing. Hence, it can be taken out commonly from the terms. d y d x = e x × ( 3 x 2 + x 3) WebFind the derivative of the function f(x) = 1/x^ Solution: The derivative of 1/x^2 is -2/x^ Find the definite integral of the function f(x) = x^2 + 3x + 2 from x = 0 to x = 1 Solution: The definite integral of x^2 + 3x + 2 from x = 0 to x = 1 can be found using the antiderivative of x^2 + 3x + 2, which is x^3/3 + 3x^2/2 + 2x. philippine travel agency in los angeles

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WebWe want two roots for f (x):= kx− 3lnx− 3, which → +∞ as x → 0+ and as x → +∞. Since f ′(x) = k − x3 vanishes only at x = k3 where f (k3) = 3ln 3k ... Is there a relationship … WebOct 20, 2015 · Explanation: The derivative of the natural log lnx is 1 x, so the derivative of 3lnx is 3 x The antiderivative of 3 x is 3lnx + C hope that helped Answer link WebThe derivative of ln(x) ln ( x) with respect to x x is 1 x 1 x. 5(x3 1 x +ln(x) d dx [x3]) 5 ( x 3 1 x + ln ( x) d d x [ x 3]) Differentiate using the Power Rule. Tap for more steps... 5(x2 + ln(x)(3x2)) 5 ( x 2 + ln ( x) ( 3 x 2)) Simplify. Tap for more … philippine travel agency chicago