First Principles Example 3: square root of x
Exploring the concept of first principles in mathematics often unveils a profound understanding of fundamental principles. An exemplary illustration of this lies in the computation of the square root of x. By breaking down the process to its most elemental components, first principles allow us to grasp the essence of extracting the square root with clarity and precision. This methodological approach fosters a deeper comprehension of mathematical operations, empowering individuals to apply foundational principles to diverse problem-solving scenarios. In this case, delving into the first principles of calculating the square root of x elucidates the underlying simplicity and elegance inherent in mathematical reasoning.
Questions
- Derivative #tan(sqrt(x))# using first principle method?
- What is the derivative of #y=sqrtx# by first principles?
- If #(1+x^2)dy/dx=x(1-y) and y(0)=4/3 #,then the value of #y(sqrt(8))+8/9# is ?
- How can you proof #intsqrt(x^2-a^2)dx# = #x/2sqrt(x^2-a^2)-a^2/2log|x+sqrt(x^2-a^2)|+C# using #x=asectheta#?
- How to calculate this? #int_0^piarcsin(cos^3x)dx#
- How do you find #f'(4)# if #f(x)=2sqrt(2x)#?
- g(x)=#int_sqrtx^xtan^(-1)tdt# Find? 1) g(#sqrt3#) 2) g'(#sqrt3#) 3) g"(#sqrt3#)
- How to differentiate ln#x/2# and ln(#√(1-#1/x#)#) respect to x?
- Is #(lnx)^2# equivalent to #ln^2 x#?
- How do you evaluate #int# #dx/(x^2sqrt(x^2 - 9))# with x = 3sec(#theta#)?
- How do you solve this problem step by step?
- How do you find the derivative of #f(x)=sqrt(x)# ?
- Differentiate the function. H(x) = (x + x^−1)^3 ?
- How do you evaluate #int# #arctan(sqrt(x))/sqrt(x)# dx?
- Derivative: find a slope of tangent line=square root of 4-5x when x=-1 ?
- How do you solve this problem step by step?
- I tried a lot to solve this question, and every time i get 2, while the correct answer is 4, HELP to solve it?
- How can you find the antiderivative of 1/(1+3x²) ?
- What is the derivative of y=ln(3x)?
- What is derivative of ln(x)?