Using the Power Rule: ddxx2= 2x ddxx3= 3x2 And so: the derivative of x2+ x3=2x + 3x2 Difference Rule What we differentiate with respect to doesn't have to bex, it could be anything. In this casev: Example: What isddv(v3−v4) ?
This derivative could not be completed using the chain rule. Mathway will use another method.Raise ( x) to the power of ( 1).( d/(df)[f(x^1x^2)((x^3-1))^(10)d])Use the power rule( a^ma^n=a^(m+n)) to combineexponents.( d/(df)[fx^(1+2)((x^3-1))^(10)d...
Differentiate using the Quotient Rule which states that ( (dw)[(f(w))(g(w))]) is ( (g(w)(dw)[f(w)]-f(w)(dw)[g(w)])((g(w))^2)) where ( f(w)=3w^4-w) and ( g(w)=w).( (w(dw)[3w^4-w]-(3w^4-w)(dw)[w])(w^2))By the Sum Rule, the derivative ...
解析 【解析】Cancel the common factor of a.d/(ds)[8/t] Since 1/t is constant with respet to s, the derivaiv of 8/x wh reset o 。is 1/td/(ds) 1/td/(ds)[s] Differentiate using the Power Rule which states tha d/(ds) s is n- whr n=1.1/t⋅1 Mutiplyby 1.1/e ...
解析 【解析】Differentiate using the Power Rule which state that d/(du)[u^n] isnu" whr n=3.3u^2 结果一 题目 【题目】Find the Derivative - d/dz 1/(z^2+1)1/(z^2+1) 答案 【解析】Rewrite1/(z^2+1) as (z^2+1)^(-1) .[(2+1)"]Differentiate using the chain rule, which...
【解析】T his derivative could not be completed using the chain rule. Mathway will use another method.Cancel the common factor of a.d/(dt)[2s⋅s/t] Combine and (2a)/t Combns and(2a)/t []Raise s to the power of 1.d/(dt)[(2(s^1si))/t] Raise s to the power of 1....
Differentiate using the Product Rule which states that ( d/(dy)[f(y)g(y)]) is ( f(y)d/(dy)[g(y)]+g(y)d/(dy)[f(y)]) where ( f(y)=e^y) and ( g(y)=y^e).( e^yd/(dy)[y^e]+y^ed/(dy)[e^y])Differentiate using the Power Rule which states that ( d/(dy)...
Find the derivative by using the chain rule. {eq}Y = \sqrt {\left( {{x^2} - 1} \right)} {/eq} Applying the Rules of Differentiation: We apply the chain rule of differentiation to differentiate a composite function. In this rule, we first differentiate the outer function...
The derivative of e^x is derived using the power rule of differentiation. This rule states that for any function f(x) = x^n, its derivative is f'(x) = nx^(n-1). When applied to e^x, the derivative becomes e^x * ln(e), which simplifies to e^x.4. What is the significance...
【解析】Differentiate using the Power Rule which states that t isn- wheren=1/2t^(1/2-1) To write -1 as a fraction with a common denominator mlily by2/2 Combn-1 and 2/2 Combine the numerators over the common denominator.11-1-2Simplify the numerator.1/2t^(1/2) Move the negative ...