Question

A) H(4) if H(x)=F(G(x)) H(4)= (b) H ′

(4) if H(x)=F(G(x)) H ′
(4)= (c) H(4) if H(x)=G(F(x)) H(4)= (d) H ′
(4) if H(x)=G(F(x)) H ′
(4)= (e) H ′
(4) if H(x)= G(x)
F(x)
​
H ′
(4)=

Answer 1

(a) H(4) if H(x)=F(G(x)): To find H(4), we need to substitute x=4 into the function H(x). Given H(x)=F(G(x)), we have H(4)=F(G(4)).

(b) H ′(4) if H(x)=F(G(x)): To find H’ (4), we need to differentiate the function H(x) and then evaluate it at x=4. Since H(x)=F(G(x)), we can use the chain rule to differentiate H(x) with respect to x. H’(x)=F’(G(x))*G’(x). Therefore, H’(4)=F’(G(4))*G’(4).

© H(4) if H(x)=G(F(x)): To find H(4), we need to substitute x=4 into the function H(x). Given H(x)=G(F(x)), we have H(4)=G(F(4)).

(d) H ′(4) if H(x)=G(F(x)): To find H’ (4), we need to differentiate the function H(x) and then evaluate it at x=4. Since H(x)=G(F(x)), we can use the chain rule to differentiate H(x) with respect to x. H’(x)=G’(F(x))*F’(x). Therefore, H’(4)=G’(F(4))*F’(4).

(e) H ′(4) if H(x)= G(x)/F(x): To find H’ (4), we need to differentiate the function H(x) and then evaluate it at x=4. Since H(x)= G(x)/F(x), we can use the quotient rule to differentiate H(x) with respect to x. H’(x)= (F(x)*G’(x) - G(x)*F’(x))/(F(x))^2. Therefore, H’(4)= (F(4)*G’(4) - G(4)*F’(4))/(F(4))^2.