Question

What is the symbol for the second derivative?

Answer 1

Hint: Differentiation is the process of derivation for the given functions or terms. Which is also the inverse of integration.
Differentiation can be defined as the derivative of the independent variable value and can be used to calculate features in an independence variance per unit modification.

Complete step-by-step solution:
Since the definition of the derivative is also known as the rate of change of a particular function.
There are several processes of differentiation: Sum and difference rule, Product rule, chain rule, and Quotient Rule.
Differentiation for the trigonometric is defined as the interaction of the angles and triangle faces, we have six major ratios sine, cosine, tangent, cotangent, secant, and cosecant.
Based on these ratios we must have interrelated trigonometric formulas like $\dfrac{{d(\sin x)}}{{dx}} = \cos x$
Hence, due to the small difference in the process of derivation, we called it a differentiation function.
So, the differentiation formula is $\dfrac{{dy}}{{dx}}$ . It shows that the difference in y is divided by the difference in x and also d is not the variable.
Hence the second derivative can be represented as $\dfrac{{{d^2}y}}{{d{x^2}}}$
Example: $\dfrac{{{d^2}({x^2})}}{{d{x^2}}} = \dfrac{{d(2x)}}{{dx}} = 2$
Additional information:
Integration is the process of inverse differentiation.
Process of finding the functions whose derivative is given named anti-differentiation or integration.
Integration is the process of adding the slices to find their whole.
It can be used to find the area, volume, and central points.
The integration is \[\int\limits_a^b {f(x)dx} \] the value of the anti-differentiation at the upper limit b and the lower limit a with the same anti-differentiation.

Note: Differentiation and integration are inverse processes like a derivative of \[\dfrac{{d({x^2})}}{{dx}} = 2x\]and the integration is $\int {2xdx = \dfrac{{2{x^2}}}{2}} \Rightarrow {x^2}$
In differentiation, the derivative of $x$ raised to the power is denoted by $\dfrac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}$ .
The inverse of the function is defined as ${x^{ - 1}} = \dfrac{1}{x}$