"The derivative of X is 1, the derivative of 5x is going to be 5."
"The derivative of sine U is cosine of that U variable times the derivative of U."
"E is the unique solution to the formula a to the x, where it is its own derivative."
"The exterior derivative is similar to the regular derivative in the sense that it essentially describes how fast an object is changing."
"Can you find the slope of a curve at a point? What was that, a derivative?"
"The derivative of x cubed is 3x squared."
"So let's find f prime, that's going to be three z squared times everything else."
"Antiderivative of 10^x is 10^x divided by natural log of 10."
"A derivative is telling you how fast something changes."
"Derivative represents the slope of the original curve at every single point."
"The derivative of any constant is zero."
"For a nice simple graph like y = x^2, that would be our expression, that is our value of dy/dx there, 2x."
"It's just an equation that has a derivative."
"We cannot isolate the Y, but we can still get the dy/dx."
"The derivative of cosine is negative sine, so we put on a negative sign, and then the input stays the same."
"The derivative of sin x is just as good as cos x."
"The derivative of cos x gives us negative sin x."
"The derivative of f of x is the limit as h tends to zero."
"Gamma is essentially a derivative of Delta."
"This is what the derivative of this function looks like."
"The left hand side of our equation is actually the derivative of a product."
"The derivative of the sine function is simply the cosine."
"The derivative of y with respect to time equals negative constant k times the state y."
"The derivative of u times v is usually written as the derivative of u times v plus u times the derivative of v."
"The derivative of a constant is 0."
"The derivative of the variable with respect to which you are taking the derivative is 1."
"At the turning point, \( f'(x) \) equals zero."
"The slope of the curve where x equals negative two is the derivative at that point."
"The derivative of 2x is 2, a constant, a positive constant, and that positive constant tells me that the curve is bending upwards."
"The derivative of a function f at a number a, denoted by f prime of a, is defined to be the limit as h goes to zero."
"The general rule here is that if you're differentiating a function of y with respect to x, the answer is the derivative of that function with respect to y, but you times by dy by dx afterwards."
"The derivative gives the slope, the rise over run, of the function for a short distance."
"The derivative is a very intuitive concept; it's the rate of change of something."
"In order to find the derivative, you do the convolution or apply a mask."
"If you differentiate the absolute value of x, what is the derivative? It's the function that we were just talking about before."
"The derivative is a function that tells you the slope of the tangent line at any point \( x \)."
"A derivative is an equation that is actually a slope function; it tells you the slope at any point to your curve."
"The derivative of \( x \) to the \( n \)th power is \( n \) times \( x \) to the \( n-1 \)th power."
"The derivative represents the rate of change of something."
"The derivative of a function f at some number a is f prime of a equals the limit as h approaches 0 of f of a plus h minus f of a all divided by h."
"If the first derivative changes from positive to negative, then you have a local max where the first derivative is zero."
"If the derivative changes from negative to positive as you move from left to right, then at this point, we have a local minimum."
"The derivative of a function at a point is a number, and that number has to do with the ratio of how fast the output of the function is growing relative to the input at that point."
"The derivative will equal zero; it has a horizontal tangent line."
"The derivative is nothing but the slope of the tangent line at a point \( (x, f(x)) \)."
"Calculus is about change, and derivative is the most important tool which encompasses that idea."
"The derivative with respect to x of c time the function is equal to c times the derivative of the function."
"The derivative of a function is the slope of its tangent at each point."
"The derivative with respect to x of the natural log of the absolute value of x is equal to 1/x."
"The derivative with respect to x of arcsin(u) is u prime over the square root of 1-u^2."
"The derivative of y with respect to x can be written as dy by dx."
"The first derivative is the rate of change of a rate of change."