A Slippery Slope
This calculus tool is related to the concept of slope at a point
What is the derivative?
d/{dx}e^x
e^x
f(x)=x
f'(x)=1
Find the equation of the tangent line at x=3 of
f(x)=5x^2
y-45=30(x-3)
This formula defines the average rate of change of a function
{f(b)-f(a)}/{b-a}
d/{dx}x^n
n*x^{n-1}
f(x)=x^6-2x^3
f'(x)=6x^5-6x^2
Find the equation of the tangent line at x=0 of
f(x)=e^x
y-1=x
This is the formal definition of the derivative using limits
f'(x)=lim_{h->0}{f(x+h)-f(x)}/h
d/{dx}\log_a(x)
1/{x\cdot\ln(a)}
f(x)=4x-\sqrt{x}
f'(x)=4-1/{2\sqrt{x}}
Find the equation of the tangent line at
x=\pi/4
f(x)=cos(x)
y-\sqrt{2}/2=-\sqrt{2}/2(x-\pi/4)
The derivative of what function is represented in this limit:
lim_{h->0}{(x+h)^4*sin(x+h)-(x^4)*sin(x)}/h
y=x^4*sin(x)
d/{dx}(f(x)\cdot g(x))
f(x)\cdot g'(x)+g(x)\cdot f'(x)
f(x)=root(6){x^5}+1/{x^2}
f'(x)=5/{6root(6){x}}-2/{x^3}
Find the equation of the normal line at x=0 of
y=e^x*\tan(x)
y=-x
What is the derivative of this function at x=0:
lim_{h->0}{sec(x+h)-sec(x)}/h
1
d/dx (f(x)/g(x))
(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2
f(x)=x^4*\sin(x)+\sqrt{x^3}*e^x
f(x)=x^4\cos(x)+4x^3\sin(x)+\sqrt{x^3}*e^x+{3\sqrt{x}}/2*e^x}
Find the equation of the normal line at x=3 of
y=\ln(x)/{x^2}
y-\ln(3)/9=-{27}/{1-2\ln(6)}(x-3)