Example

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

Question

$$F(x)= \frac{ COS(3x) \times SENH(4 { x }^{ 2 } ) }{ { E }^{ 2x } IN(x) }$$

Answer

$$F=(COS3*SENH4*x^2)/(INx*E^(2*x))$$

Solution


Remove parentheses.
\[Fx=\frac{COS3xSENH4{x}^{2}}{{E}^{2x}INx}\]
Regroup terms.
\[Fx=\frac{x{x}^{2}COS3SENH4}{{E}^{2x}INx}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[Fx=\frac{{x}^{1+2}COS3SENH4}{{E}^{2x}INx}\]
Simplify  \(1+2\)  to  \(3\).
\[Fx=\frac{{x}^{3}COS3SENH4}{{E}^{2x}INx}\]
Regroup terms.
\[Fx=\frac{COS3SENH4{x}^{3}}{{E}^{2x}INx}\]
Regroup terms.
\[Fx=\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}}\]
Divide both sides by \(x\).
\[F=\frac{\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}}}{x}\]
Simplify  \(\frac{\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}}}{x}\)  to  \(\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}x}\).
\[F=\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}x}\]
Simplify  \(\frac{COS3SENH4{x}^{3}}{INx{E}^{2x}x}\)  to  \(\frac{COS3SENH4{x}^{2}}{INx{E}^{2x}}\).
\[F=\frac{COS3SENH4{x}^{2}}{INx{E}^{2x}}\]
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