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An equation involving a derivative is known as a differential equation. You need to be able to form differential equations using information given in a question. You also need to be able to apply the chain rule to problems involving rates of change, where there are more than two variables involved.
Evaluate f ( x ) at all points found in Step 1. minimum, or neither if f ¢¢ ( c ) = 0 . Evaluate f ( a ) and f ( b ) . Identify the abs. max. (largest function value) and the abs. min.(smallest function value) from the evaluations in Steps 2 & 3.
Derivatives Rules. Power Rule \frac {d} {dx}\left (x^a\right)=a\cdot x^ {a-1} Derivative of a constant \frac {d} {dx}\left (a\right)=0. Sum Difference Rule \left (f\pm g\right)^'=f^'\pm g^'.
Basic Properties and Formulas. If f ( x ) and g ( x ) are differentiable functions (the derivative exists), c and n are any real numbers, ( c f ) ′ = c f ′ ( x ) ( f ± g ) ′ = f ′ ( x ) ± g ′ ( x ) ( f g ) ′ = f ′ g + f g ′ – Product Rule. f ′ f ′ g − f g ′.
This document provides rules and formulas for taking derivatives of common functions including: - The power rule for derivatives of functions with exponents - Rules for sums, differences, products and quotients of functions - Derivatives of trigonometric, inverse trigonometric, hyperbolic, inverse hyperbolic, exponential and logarithmic ...
Derivative Rules and Formulas Rules: (1) f 0(x) = lim h!0 f(x+h) f(x) h (2) d dx (c) = 0; c any constant (3) d dx (x) = 1 (4) d dx (xp) = pxp 1; p 6= 1 (5) d dx [f(x) g(x)] = f0(x) g0(x) (6) d dx (cf(x)) = cf0(x) (7) d dx [ f x)g)] = )+ (8) d dx f(x) g(x) = f0(x)g(x) f(x)g0(x) (g(x))2 (9) d dx 1 g(x) = g0(x) (g(x))2 (10) d dx [ f (g x))] = 0 ...
Derivatives Cheat Sheet. Derivative Rules. Constant Rule: (c) = 0; where c is a constant dx. 2. Power Rule: (xn) = nxn 1 dx. 3. Product Rule: (fg)0 = f0g + fg0. 4. Quotient Rule: f 0 f0g. = fg0. g g2. 5. Chain Rule: (f(g(x))0 = f0(g(x))g0(x) Exponential & Logarithmic Functions. d. (ax) = ax ln(a) dx. d. (ex) = ex dx. d 1. (log a(x)) = dx x ln(a)
