first derivative of the given function

\(y= 6 sec 3x \)

Your answer

asked 2022-01-06

first derivative of the given function

\(y= 6 sec 3x \)

asked 2021-08-08

a. Locate the critical points of ƒ.

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}}}{{{x}^{{{2}}}-{1}}}}\) on \(\displaystyle{\left[-{4},{4}\right]}\)

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}}}{{{x}^{{{2}}}-{1}}}}\) on \(\displaystyle{\left[-{4},{4}\right]}\)

asked 2022-01-02

How to find first derivative of function \(\displaystyle{y}={x}{\ln{{\left({x}\right)}}}\) by limit definition, that is using this formula

\(\displaystyle{y}'=\lim_{{{h}\to{0}}}{\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}}\)

\(\displaystyle{y}'=\lim_{{{h}\to{0}}}{\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}}\)

asked 2021-09-11

Use the limit definition of the derivative to calculate the derivatives of the following function:

(a) \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}+{3}{x}+{1}\)

(b) \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{2}}}{{{x}^{{2}}}}}\)

(a) \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}+{3}{x}+{1}\)

(b) \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{2}}}{{{x}^{{2}}}}}\)

asked 2021-06-08

Use the limit definition of the derivative to calculate the derivatives of the following function:

(a) \(f(x)=4x^2+3x+1\)

(b) \(f(x)=\frac{2}{x^2}\)

(a) \(f(x)=4x^2+3x+1\)

(b) \(f(x)=\frac{2}{x^2}\)

asked 2022-01-12

Explain how to apply the First Derivative Test.

asked 2021-12-09

Find the first derivative of \(\displaystyle{e}^{{{x}^{{{2}}}}}\)