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Learn how to solve differential calculus problems step by step online. Find the derivative of y=tan(x)^(5/x). Apply natural logarithm to both sides of the equality. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Derive both sides of the equality with respect to x. Multiplying the fraction by \ln\left(\tan\left(x\right)\right).
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.