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Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...
In the table below, ? œ 0ÐBÑ and @ œ 1ÐBÑ represent differentiable functions of B. ) -? ( . œ ! . B .- œ - .? Ð We could also write Ð-0Ñ w œ -0 w , and could use the “prime notion” in the other formulas as well) . ( ? „ @ ) œ „ .? .@ . B .B .B.
Differentiation Formulas Suppose f and g are differentiable functions. Constant Rule: d dx (c) = 0 Power Rule: d dx (xn) = nxn−1 for any real number n Constant Multiple Rule: d dx [cf(x)] = cf0(x) for any constant c Sum Rule: d dx [f(x)+g(x)] = f0(x)+g0(x) Difference Rule: d dx [f(x)−g(x)] = f0(x)−g0(x) Product Rule: d dx [f(x)g(x ...
Basic Properties and Formulas. ( cf ) ′ = cf ′ ( x ) ( f ± g ) ′ = f ′ ( x ) + g ′. (. x ) Product rule. ( f ⋅ g ) ′ = f ′ ⋅ g + f ⋅ g ′. Quotient rule.
Basic differentiation and integration formulas. # 1 Derivatives. Memorize. (xn) = nxn−1 dx. 1. (ln x) = dx x. (ex) = ex dx. (sin x) = cos x dx. (cos x) = − sin x dx. (tan x) = sec2 x dx. (cot x) = − csc2 x dx. (sec x) = sec x tan x dx. (csc x) = − csc x cot x dx. (tan–1 1. x) = dx 1 + x2. (sin–1. 1 dx. x) = p1 − x2. # 2 Antiderivatives.
Okay, so we know the derivatives of constants, of x, and of x2, and we can use these (together with the linearity of the derivative) to compute derivatives of linear and quadratic functions. To compute the derivatives of all polynomials, we’d need to know the derivatives of xn for higher n. How can we do this? Let’s start with an example: d ...
List of Derivative Rules. Below is a list of all the derivative rules we went over in class. Constant Rule: f(x) = c then f0(x) = 0. Constant Multiple Rule: g(x) = c · f(x) then g0(x) = c · f0(x) Power Rule: f(x) = xn then f0(x) = nxn−1.
