differentiation

A fifth-degree polynomial in $x$ is defined for $x > 0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at a point...

Let $f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix}$ where $p$ is a constant. The value of $\frac{d^3}{dx^3} f(x)$ at $x = 0$ is

Consider the function given below and pick one or more CORRECT statement(s) from the following choices. f(x) = x³ − (15/2)x² + 18x + 20

Consider the following expression: z = sin(y + it) + cos(y $$-$$ it) where z, y, and t are variables, and $$i = \sqrt { - 1} $$ is a complex number. The partial differential equati...

The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

The value of $$\varepsilon $$ in the mean value theoram of $$f\left( b \right) - f\left( a \right) = \left( {b - a} \right)\,\,f'\left( \varepsilon \right)$$ for $$f\left( x \right...