导数题设f(5)=5,f'(5)=3,g(5)=4,g'(5)=1在下列情况下求h(5)和h'(5)设f(5)=5,f'(5)=3,g(5)=4,g'(5)=1在下列情况下求h(5)和h'(5)(1)h(x)=3f(x)+2g(x)(2)h(x)=f(x)g(x)+1(3)h(x)=[f(x)+2]/g(x)

Question

导数题 设f(5)=5,f'(5)=3,g(5)=4,g'(5)=1在下列情况下求h(5)和h'(5)
设f(5)=5,f'(5)=3,g(5)=4,g'(5)=1在下列情况下求h(5)和h'(5)(1)h(x)=3f(x)+2g(x)(2)h(x)=f(x)g(x)+1(3)h(x)=[f(x)+2]/g(x)

Answer 1

(1)h(x)=3f(x)+2g(x)h(5)=3f(5)+2g(5)=3*5+2*4=23h'(5)=3f'(5)+2g'(5)=3*3+2*1=11(2)h(x)=f(x)g(x)+1h(5)=f(5)g(5)+1=5*4+1=21h'(5)=f'(5)g(5)+f(5)g'(5)=3*4+5*1=17(3)h(x)=[f(x)+2]/g(x)h(5)=(f(5)+2)/g(5)=(5+2)/4=7/4h'(5)=f'(5)/g(5)-(f(5)+2)/[g'(5)]^2=3/4-(5+2)/1^2=3/4-7=-25/4