Find the derivative of $u(x)=-4\ln x-5x^2$, for $x>0$.

Find the derivative of $g(x)=-8e^x+5x^6$.

Let $f(x)=\frac{x^2+3x-54}{x-6}$. Which condition for continuity at $x=6$ fails?

A particle has position $s(t)=2t^3+3t^2-12t$ meters at time $t$ seconds. Find the acceleration at $t=1$.

At which value of $x$ does $q(x)=\frac{(x-2)(x-5)}{(x-2)(x+2)}$ have a REMOVABLE discontinuity?

Find the average rate of change of $f(x)=-2x^2-8x+5$ on the interval $\left[3,7\right]$.

A cube is heated so that each edge grows at $4$ centimeters per second, with $V=s^3$. How fast is the volume changing when each edge is $7$ centimeters long? Give the answer in cubic centimeters per second.

A circular ripple spreads so that its radius grows at $5$ centimeters per second, with $A=\pi r^2$. How fast is the area changing when the radius is $5$ centimeters? Give the answer in square centimeters per second.

Evaluate ${\lim }_{x\to \infty }\frac{3x^2-4x}{-9x^2-4}$.

Evaluate ${\lim }_{x\to 3^{+}}\frac{x-2}{x-3}$.

Evaluate ${\lim }_{x\to -1}\frac{x^2+8x+7}{x^2-x-2}$.

A particle has position $s(t)=2t^3+3t^2-72t$ at time $t$. Is it speeding up or slowing down at $t=1$?

The point $\left(-6,2\right)$ lies on the curve $x^2-9y^2=0$. What is the slope of the curve there?

Find the equation of the line tangent to $p(x)=-4x^2-2x$ at $x=1$.

Find the derivative of $v(x)=-8x^6-x$.

On which set is $g(x)=2x^3+12x^2+18x$ CONCAVE DOWN?

For $f(x)=2x^3-3x^2-12x$, use the Second Derivative Test to classify the critical point at $x=2$.

A spherical balloon is inflated so that its radius grows at $5$ centimeters per second, with $V=\frac{4}{3}\pi r^3$. How fast is the volume changing when the radius is $4$ centimeters? Give the answer in cubic centimeters per second.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{6x}$, with $x$ in radians.

Find the derivative of $g(x)=\frac{-6x-5}{-4x+1}$.

Find the derivative of $r(x)=-6x^{-7}$.

Evaluate ${\lim }_{x\to -5}\frac{x^2+9x+20}{x^2+x-20}$.

Let $M(t)$ be the mass of a culture after $t$ days, in grams. What are the units of $M^{\prime }\left(t\right)$?

Let $v(x)=\frac{x^2-4x-45}{x-9}$. Which condition for continuity at $x=9$ fails?

Find $\frac{dy}{dx}$ for the relation $3x^2-7y^2=-9$.

Find the equation of the line normal to $r(x)=-3x^2+5x$ at the point $\left(-6,-138\right)$.

A particle has position $s(t)=2t^3-9t^2+12t$ at time $t$. Is it speeding up or slowing down at $t=-3$?

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{7x}$, with $x$ in radians.

Find the derivative of $u(x)=\cos \left(-2x^2+8\right)$, with $x$ in radians.

Use the definition $f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ to find $f^{\prime }(x)$ for $f(x)=6x^2+9x+9$.

Find the average rate of change of $q(x)=3x^2-8x+5$ on the interval $\left[-3,1\right]$.

Let $g(x)=\{\begin{array}{ll}3x+k& x<-1\\ x^2+6& x\ge -1\end{array}$. For what value of $k$ is $g$ continuous at $x=-1$?

Evaluate ${\lim }_{x\to \infty }\frac{7x+3}{x^2+7}$.

Find the derivative of $f(x)={\left(5x^4-5\right)}^7$.

Find the derivative of $r(x)=8x^3+2x^2-6x+9$.

Find the derivative of $f(x)=\left(4x^2+6\right)\left(4x-1\right)$.

A particle has position $s(t)=2t^3-24t$ at time $t$. Is it speeding up or slowing down at $t=4$?

On which set is $v(x)=2x^3-12x^2+18x$ CONCAVE UP?

Find the derivative of $w(x)=7x^3+4x^2-3x-9$.

Find the derivative of $g(x)={\left(-6x^3-7\right)}^7$.