Use logarithmic differentiation to find the derivative of the function y = (cosx) ^x

Question

Jesus Greene

Mathematics

8 March, 16:36

Use logarithmic differentiation to find the derivative of the function y = (cosx) ^x

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Kailey · Answer 1

Y=cos (x) ^ (x)

Applying log on both sides

ln (y) = xln[cos (x) ]

Differentiating w. r. t x

dy/dx/y=ln[cos (x) ] d/dx 1 + x d/dx 1 / (cos (x)) d/dx - sin (x)

dy/dx=cos (x) ^x[ln[cos (x) ] - xtan (x) ]