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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. Sum and Difference Rule: h(x) = f(x)±g(x) then h0(x) = f0(x)±g0(x)
1. Introduction. In this unit we learn how to differentiate a ‘function of a function’. We first explain what is meant by this term and then learn about the Chain Rule which is the technique used to perform the differentiation. 2. A function of a function. Consider the expression cos x2.
Integration Formulas Z dx = x+C (1) Z xn dx = xn+1 n+1 +C (2) Z dx x = ln|x|+C (3) Z ex dx = ex +C (4) Z ax dx = 1 lna ax +C (5) Z lnxdx = xlnx−x+C (6) Z sinxdx = −cosx+C (7) Z cosxdx = sinx+C (8) Z tanxdx = −ln|cosx|+C (9) Z cotxdx = ln|sinx|+C (10) Z secxdx = ln|secx+tanx|+C (11) Z cscxdx = −ln |x+cot +C (12) Z
Rules: f0(x) = lim f(x + h) f(x) h!0 h. d. (c) = 0; c any constant dx. d. (x) = 1 dx. d. (xp) = p xp 1; p 6= 1 dx.
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 ...
Derivative of a constant Derivative of constant multiple Derivative of sum or difference. ) -? ( . œ ! . B .- œ - .? .B .B. 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.
Diferentiation Formulas. General Formulas. : . c = . d −. 2. Power Rule: 1 , x dx. n. . d. 3. Scalar Multiple of a Function: c f ( dx. dx. 5. Product Rule: f ( x ) g ( f ( x ) g ( x ) + g ( x ) f ( x ) dx x ) = g. 6. Quotient Rule: ( ) = 2. g. d. 7. Chain Rule: f ( g ( x ) ) = f g ( x ) g ( x ) dx.
