Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{d}{d\ \sin\ x}(\sin\ x)^{5}$$

Answer

$$sin(x)^4$$

Solution


Remove parentheses.
\[\frac{d}{d\sin{x}}\sin^{5}x\]
Cancel \(d\).
\[\frac{1}{\sin{x}}\sin^{5}x\]
Use this property: \(\sin{x}=\frac{1}{\csc{x}}\).
\[\csc{x}\sin^{5}x\]
Use this property: \(\csc{x}=\frac{1}{\sin{x}}\).
\[\sin^{4}x\]
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