• Power Rule: f(x)=xn thenf0(x)=nxn−1 • Sum and Difference Rule: h(x)=f(x)±g(x)thenh0(x)=f0(x)±g0(x) • Product Rule: h(x)=f(x)g(x)thenh0(x)=f0(x)g(x)+f(x)g0(x) • Quotient Rule: h(x)= f(x) g(x) thenh0(x)= f0(x)g(x)−f(x)g0(x) g(x)2 • Chain Rule: h(x)=f(g(x))thenh0(x)=f0(g(x))g0(x) • Trig Derivatives: – f(x)=sin(x)thenf0(x)=cos(x)
Differentiation Rules While it’s possible to compute derivatives using the definition of the derivative as a limit, it is too much work if you’re differentiating anything complicated. It’s more efficient to develop a set of differentiation rules to use as shortcuts. Before we start, here are several comments.
Basic Differentiation and Integration Rules Basic Integration Rules References - The following work was referenced to during the creation of this handout: Summary of Rules of Differentiation. For basic integration rules, refer to the URL: https://d2vlcm61l7u1fs.cloudfront.net/media/085/08537e59-da37-4271-b5f6-ca4eadfc6048/phpIarHol.png
Proofs of Differentiation Rules Covered: Four rules of derivatives (i.e. +,−,×,÷) Briefly Mention Chain Rule (i.e. derivative of composite function of two functions) Four rules of derivatives Assumption: In the following let ( ), ( ) be two functions, both having the same
Students are advised to equip themselves with the following rules to be able to apply them in the subsequent topics like marginal analysis, optimisation (Unconstrained and Constrained) problems. Following are some of the rules of Differentiation. 1. Constant Function Rule. ) = ( , where A is a constant, is zero.
Basic Derivative Rules (using Leibniz notation) • Derivative of a constant function f(x) = c: d dx [c] = 0 • Power Rule f(x) = xn, n is any real number (very nice proof we will look at in Section 3.6): d dx [xn] = nx(n−1) • The Constant Multiple Rule: if c is a constant and f is a differentiable function: d dx [cf(x)] = c d dx f(x)
The basic rules of difierentiation, as well as several common results, are presented in the back of the log tables on pages 41 and 42. Rule 1: The Derivative of a Constant. The derivative of a constant is zero. Rule 2: The General Power Rule. The derivative of xn is nxn¡1. Example 1 Difierentiate y = x4. If y = x4 then using the general ...
2.5 Basic Differentiation Rules • Find derivatives using basic rules of differentiation for polynomial, power, sine, cosine, tangent, exponential and logarithmic functions. 9. 10: 2.6 Product and Quotient Rules • Apply the product and quotient rules algebraically for polynomial, power, sine, cosine, tangent, exponential and logarithmic ...
DIFFERENTIATION RULES Once you know how to differentiate basic functions (see sepa-rate worksheet if necessary) you need to be able to combine them into more complicated examples. The fundamental rules are as follows. sums and differences d dx (u± v) = du dx ± dv dx constant multiple d dx (cu) = c du dx product rule d dx (uv) = u dv dx +v ...
Basic Differentiation Rules • All rules are proved using the definition of the derivative: • The derivative exists (i.e. a function is differentiable) at all values of x for which this limit exists. € df dx =f'(x)=lim h→0 f(x+h)−f(x) h
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