Αποτελέσματα Αναζήτησης
www.mathportal.org 3. Higher-order Derivatives Definitions and properties Second derivative 2 2 d dy d y f dx dx dx ′′ = − Higher-Order derivative
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.
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.
Differentiation Formulas. Derivatives of Basic Functions. Derivatives of Logarithmic and Exponential Functions. Derivatives of Trigonometric Functions. Derivatives of Inverse Trigonometric Functions.
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 ...
Differentiation Formulas General Formulas 1. Constant Rule: >@0 d c dx 2. Power Rule: dx nxnn1 dx ªº ¬¼, x 3. Scalar Multiple of a Function: dx dx ªº¬¼ c 4. Sum and Difference of Functions: d f x gx f x g x cc dx ªº¬¼r r 5. Product Rule: d f x gx f x gx g x f x cc dx ªº¬¼ 6. Quotient Rule: 2 d x
