求导函数!不需要全部展开第一个:f(x)=[(3x-8)^2+(2-x)^5]^2第二个:f(x)=(x/4.6+4.6/x)(x^2+1)第三个:f(x)=(x^2-8x)^-2*(1-x^2)^0.5最后一道应用题,是用g(f(x))=g'(f(x))*f'(x)来解的.The weekly revenue from the sale of emeral

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 08:02:12

求导函数!不需要全部展开第一个:f(x)=[(3x-8)^2+(2-x)^5]^2第二个:f(x)=(x/4.6+4.6/x)(x^2+1)第三个:f(x)=(x^2-8x)^-2*(1-x^2)^0.5最后一道应用题,是用g(f(x))=g'(f(x))*f'(x)来解的.The weekly revenue from the sale of emeral
求导函数!不需要全部展开
第一个:f(x)=[(3x-8)^2+(2-x)^5]^2
第二个:f(x)=(x/4.6+4.6/x)(x^2+1)
第三个:f(x)=(x^2-8x)^-2*(1-x^2)^0.5
最后一道应用题,是用g(f(x))=g'(f(x))*f'(x)来解的.
The weekly revenue from the sale of emeralds at Eduardo's Emerald Emporium (EEE) is decreasing at a rate of €450 per €1 increase in price, and the price is decreasing at a rate of €0.42 per additional emerald sold. What is the marginal revenue?
最后一道应用题可以不解答~

求导函数!不需要全部展开第一个:f(x)=[(3x-8)^2+(2-x)^5]^2第二个:f(x)=(x/4.6+4.6/x)(x^2+1)第三个:f(x)=(x^2-8x)^-2*(1-x^2)^0.5最后一道应用题,是用g(f(x))=g'(f(x))*f'(x)来解的.The weekly revenue from the sale of emeral
第一个:f(x)=[(3x-8)^2+(2-x)^5]^2
f(x)'=2*[(3x-8)^2+(2-x)^5]*(2*(3x-8)*3+5*(2-x)^4*(-1))
=2*[(3x-8)^2+(2-x)^5]*(6*(3x-8)-5*(2-x)^4)
第二个:f(x)=(x/4.6+4.6/x)(x^2+1)
=((x^2+4.6^2)/(4.6*x)(x^2+1)
=(x^2+4.6^2)*(x^2+1)*(4.6*x)^(-1)
f(x)'=2x*(x^2+1)*(4.6*x)^(-1)+2x*(x^2+4.6^2)*(4.6*x)^(-1)+(-1)*4.6*(x^2+4.6^2)*(x^2+1)*(4.6*x)^(-2)
=x*(x^2+1)*(2.3*x)^(-1)+x*(x^2+4.6^2)*(2.3*x)^(-1)-4.6*(x^2+4.6^2)*(x^2+1)*(4.6*x)^(-2)
=x*(2*x^2+4.6^2+1)*(2.3*x)^(-1)-4.6*(x^2+4.6^2)*(x^2+1)*(4.6*x)^(-2)
=x*(2*x^2+4.6^2+1)/(2.3*x)-4.6*(x^2+4.6^2)*(x^2+1)/(4.6*x)^2
=x*(2*x^2+4.6^2+1)/(2.3*x)-(x^2+4.6^2)*(x^2+1)/(4.6*x^2)
第三个:f(x)=(x^2-8x)^(-2)*(1-x^2)^0.5
f(x)'=(-2)*(x^2-8x)^(-3)*(2x-8)*(1-x^2)^0.5+(x^2-8x)^(-2)*(-2*x)*0.5*(1-x^2)^(-0.5)
=(-2)*(x^2-8x)^(-3)*(2x-8)*(1-x^2)^0.5-(x^2-8x)^(-2)*x*(1-x^2)^(-0.5)