Popular questionsPage 19

velocity v(t)=2t^2-6t+5 integer time slowing down

cube side length increasing at 1/3 inch per second volume rate

Evaluate lim x→3 (g(2x+1)-5)/(x^2-9)

If the position of a particle is $x(t)=t^2-4t+5$, at what time is the particle at rest?

Approximate the value of $g(6)$ using the tangent line to $g(x)$ at $x=5$

Evaluate the limit $\lim_{x\to 3}\frac{g(2x+1)-5}{x^2-9}$

Chain rule for $$\frac{d}{dx}\left(\frac{-16x}{2y}\right)$$

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 $v(2)$

Theorem 2. Let $s_0 = \sigma_0 + i t_0$ be a fixed complex number