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(Solved): Answer all questions. Name: ICA-5 M&151 Hybrid Ch. 3.1 Derivatives of Polynomials and Exponential Fu ...
Answer all questions.
Name: ICA-5 M&151 Hybrid Ch. 3.1 Derivatives of Polynomials and Exponential Functions 1. From the definition of the derivative, prove the following basic rules of derivatives. Assume f, g are differentiable functions and c is a scalar: (a)(c-f(x))=c(f(x)) (c)(c)=0 (b)(-9)(x) = (f(x))-(g(x)) (d) (cz)=c
2. The derivative of an exponential function with base b, f(x)=b is (b)-In(b)b. (a) If f(x)=b find the first three derivatives of f. (b) What is the nth derivative of f? (e) Find the normal line to y=at z=0. Note: The normal line is perpendicular to the tangent line at the point of tangency.
3. Use the equation of the derivative of an exponential function to find the derivative of the exponential function with base e. Repeat the exercise using the limit definition of the derivative, what is the value of lim A-0 h