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Solving: ddx(y=ln⁡(x)sin⁡(x))\frac{d}{dx}\left(y=\ln\left(x\right)^{\sin\left(x\right)}\right)
Solve instead: dydx(y=(lnx)sinx)\frac{dy}{dx}\left(y=\left(lnx\right)^{sinx}\right)
y=ln(x)^sin(x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

dydx(y=(lnx)sinx)\frac{dy}{dx}\left(y=\left(lnx\right)^{sinx}\right)

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Final answer to the exercise

y′=(cos⁡(x)ln⁡(ln⁡(x))+sin⁡(x)xln⁡(x))ln⁡(x)sin⁡(x)y^{\prime}=\left(\cos\left(x\right)\ln\left(\ln\left(x\right)\right)+\frac{\sin\left(x\right)}{x\ln\left(x\right)}\right)\ln\left(x\right)^{\sin\left(x\right)}

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dydx (y=(lnx)sinx)
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