William Anthony Granville

“ Ans. In differentiating an exponential function, especially a variable with a variable exponent, the best plan is first to take the logarithm of the function and then differentiate. Thus Illustrative Example 5, p. ”

“ When , and IX becomes IXa . The derivative of a constant with a variable exponent is equal to the product of the natural logarithm of the constant, the constant with the variable exponent, and the derivative of the exponent.
46. Differentiation of the general exponential function.
Let . [4] Taking the logarithm of both sides to the base , , or, . Differentiating by formula Ixa, by V X ∴ . 'The derivative of a function with a variable exponent is equal to the sum of the two results obtained by first differentiating by VI, regarding the exponent as constant,. ”

“ Solution: by X Ans. 47. Logarithmic differentiation. Instead of applying VIII and VIIIa at once in differentiating logarithmic functions, we may sometimes simplify the work by first making use of one of the formulas 7-10 on p. ”