The derivative of ₁₀ x with respect to _x 10 is

Step-by-step solution

Let u = ₁₀ x and v = _x 10 . Using the base change property of logarithms, v = 1 ₁₀ x = 1 u . Differentiating v with respect to u , we get dv du = - 1 u^2 . The derivative of u with respect to v is given by du dv = 1 dv du . Substituting the value of dv du , we get du dv = -u^2 . Replacing u with ₁₀ x , we obtain du dv = -( ₁₀ x)^2 . Answer: -( ₁₀ x)^2