# Posts for Tag: Differentiation

### Application of Differentiation – HSC Math

if \$(x,y) is a point over line \$y=f(x)\$ and the slope of the line at that point \$(x,y)\$ is θ\$, then- \$tan\ θ=\d/\dy(y)\$ here, the tangent of the line at point \$(x,y)\$ creates θ° angle with \$x\ axis\$. If the tangent of a line is parallel to \$x\ axis\$ or perpendicular to \$y\ axis\$ then-Read More

### Multiple Times Differentiation – HSC Math

if \$y=f(x),\$ then \$\d/{\dx}(y)=\dy/{\dx}=f'(x)=y′=y_1\$ \$\d/{\dx}(y_1)=\d^2y/{\dx^2}=y_2\$ \$\d/{\dx}(y_2)=\d^3y/{\dx^3}=y_3\$ \$\d/{\dx}(y_{n-1})=\d^ny/{\dx^n}=y_n\$ if \$y=e^{mx}, y_n=m^n\ e^{mx}\$ if \$y=a^x, y_n=a^x\ (log_e\ a)^n=a^x\ (ln\ a)^n\$ if \$y=sin(ax+b), y_n=a^n\ sin(n.π/2+(ax+b))\$ if \$y=cox(ax+b), y_n=a^n\ cos(n.π/2+(ax+b))\$

### Differentiation Formulas – HSC Math

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. if \$y=f(x)\$ is a function, then its first derivative, i.e. \${\dy}/{\dx}=f'(x)=\lim↙{h→0}{f(x+h)-f(x)}/h\$ GeneralRead More