Sec3.1:DER/VATIVESofPolynomialandExponentialConstantfunctionQ[c] = 0dxExample:f(x) = 5,g(x)= 10Find :f'(x),g'(x)
f (x) = 5, g(x) =10 Find : f '(x) , g'(x) c = 0 dx d Sec 3.1: DERIVATIVES of Polynomial and Exponential Example: Constant function
Sec3.1:DER/VATIVESofPolynomialandExponentialThe power Rulenxn--dhExample:f(x)= x,g(x)= x2,h(x)= xFind :f'(x),g'(x)
2 5 f (x) = x, g(x) = x ,h(x) = x Find : f '(x) , g'(x) −1 = n n x nx dx d Example: The power Rule Sec 3.1: DERIVATIVES of Polynomial and Exponential
Sec3.1:DER/VATIVESofPolynomialandExponentialThe powerRulenxn-idExample:f(x)=二,g(x) = ~xxFind :f(x) ,g'(x)Example:f(x)= x/xFind: f'(x)
Find : f '(x) , g'(x) −1 = n n x nx dx d Example: The power Rule g x x x f x = , ( ) = 1 ( ) Find : f '(x) Example: f (x) = x x Sec 3.1: DERIVATIVES of Polynomial and Exponential
Sec3.1:DER/VATIVESofPolynomialandExponentialTheconstantmultipleO[cf(x)]= cf'(x)dxExample:f(x) = 3x4Find: f(x) ,g'(x)
cf (x) cf '(x) dx d = 4 f (x) = 3x Find : f '(x) , g'(x) Example: The constant multiple Sec 3.1: DERIVATIVES of Polynomial and Exponential
Sec3.1:DER/VATIVESofPolynomialandExponentialThesumanddiffernceRuleO[f(x)+g(x)= f'(x) +g'(x)dxq[f(x)-g(x)]= f'(x)-g'(x)dxExample:f(x)=6x4 +9x3 -20x2 +3x +8Find : f'(x) ,g'(x)
f (x) g(x) f '(x) g'(x) dx d + = + ( ) 6 9 20 3 8 4 3 2 f x = x + x − x + x + f (x) g(x) f '(x) g'(x) dx d − = − Find : f '(x) , g'(x) Example: The sum and differnce Rule Sec 3.1: DERIVATIVES of Polynomial and Exponential