Skip to main content
Textbookish

Question 9.30

Solutions

TZ
leumasicOfficial

3 months ago

i)

f′(x)=nxn−1if f(x)=xn.f'(x)=nx^{n-1}\quad\text{if } f(x)=x^n.

ii)

z′(y)=−1y2if z=1y.z'(y)=-\frac{1}{y^2}\quad\text{if } z=\frac{1}{y}.

iii)

g′(x)=f′(x)if g(x)=f(x)+c.g'(x)=f'(x)\quad\text{if } g(x)=f(x)+c.

iv)

g′(x)=cf′(x)if g(x)=cf(x).g'(x)=cf'(x)\quad\text{if } g(x)=cf(x).

v)

z′(x)=y′(x)if z(x)=y(x)+c.z'(x)=y'(x)\quad\text{if } z(x)=y(x)+c.

vi)

g′(a2)=3a4if g(x)=x3.g'(a^2)=3a^4\quad\text{if } g(x)=x^3.

vii)

g′(b)=f′(b+a)if g(x)=f(x+a).g'(b)=f'(b+a)\quad\text{if } g(x)=f(x+a).

viii)

g′(b)=cf′(cb)if g(x)=f(cx).g'(b)=cf'(cb)\quad\text{if } g(x)=f(cx).

ix)

g′(x)=cf′(cx)if g(x)=f(cx).g'(x)=cf'(cx)\quad\text{if } g(x)=f(cx).

x)

f(k)(x)=k!(nk)xn−kif f(x)=xn.f^{(k)}(x)=k!{n\choose k}x^{n-k}\quad\text{if } f(x)=x^n.
0
Submit a solution
Optional • Markdown

Sign in to share your solution for this question.

Sign in

Navigate

Q 9.30

PrevNext

Navigate

Q 9.30

PrevNext