Question

use the general power rule to find the differential coefficient of (1-x^2)^5​

Answer 1

Answer:

The Power rule also allows us to differentiate expressions like \sqrt x

x

square root of, x, end square root or x^{^{\frac{2}{3}}}x

3

2

x, start superscript, start superscript, start fraction, 2, divided by, 3, end fraction, end superscript, end superscript. Consider this differentiation of \sqrt x

x

square root of, x, end square root:

\begin{aligned} \dfrac{d}{dx}\sqrt x&=\dfrac{d}{dx}\left(x^{^{\Large\frac{1}{2}}}\right)\quad\gray{\text{Rewrite as power}} \\\\ &=\dfrac{1}{2}\cdot x^{^{\Large-\frac{1}{2}}}\quad\gray{\text{Power rule}} \\\\ &=\dfrac{1}{2\sqrt x}\quad\gray{\text{Rewrite as radical}} \end{aligned}

dx

d

x

=

dx

d

⎝

⎜

⎛

x

2

1

⎠

⎟

⎞

Rewrite as power

=

2

1

⋅x

−

2

1

Power rule

=

2

x

1

Rewrite as radical

Answer 2

Answer:

1 - x power 10 . hope you understand well .