Calculus — popular questionsPage 6

Consider the curve $y^2+8x^2=1$. Find $\frac{dy}{dx}$ at the point $(0,-1)$

If $r(x)=\sin^2(3x)$, find the slope of the tangent line at $x=\frac{\pi}{6}$

If $q(x)=\arcsin(x)+(2x-1)^3$, find the instantaneous rate of change of $q(x)$ at $x=0$

If $m(x)=\frac{g(3x-2)}{4x}$, what is the instantaneous rate of change at $x=2$?

If $k(x)=g(x)\cdot f'(7x)$, what is the slope of the tangent line at $x=1$?

Consider the curve $xy-2x=-9$. Evaluate $\frac{dy}{dx}$ at $(1,-7)$

If $j(x)=e^{2x-2}+2n(x^2+x)$, find $j'(1)$

If $h(x)=f(g(x))$, find $h'(9)$

Derivative and related calculus expressions

Find the values of a and b such that $h(x)=\begin{cases}ax^2+7x & x<1\\ 2x+b & x\ge 1\end{cases}$ differentiable at $x=1$

If $p(x)=3x\cos(x)+2x$, find $p'(0)$

If $f(x)=4h(x)+6x$, find $v(2)$

Simplify $\sqrt{-81x^4y^2}$

Rewrite the radical expression as an exponential expression: $\sqrt{3-y^2}$

Rewrite the radical expression as an exponential expression: $4y\sqrt{x^7}$

Rewrite the radical expression as an exponential expression: $-\sqrt[3]{2x^8}$

Solve $y'' + e^y = 0$

Question 6. A point $P(x,y)$ is on the circle

(a) Show that one possible value of $a$ is and the other possible value is

L : Ax+By+C=0