Question

$y=5x^{7/2}-2x^{3/2}+4x^{-3/2}-8x^{-5/2}$ find the value of $\frac{dy}{dx}$

Answer 1

Given that,

$y=5x^{\frac{7}{2}}-2x^{\frac{3}{2}}+4x^{\frac{-3}{2}}-8x^{\frac{-5}{2}}$

Now, on differentiate

$\frac{dy}{dx}=\frac{7}{2}\times 5x^{\frac{7}{2}-1}-2\times \frac{3}{2}{x}^{\frac{3}{2}-1}+4\times \frac{-3}{2}{x}^{\frac{-3}{2}-1}-8\times \frac{5}{2}{x}^{\frac{5}{2}-1}$

$\frac{dy}{dx}=\frac{35}{2}{x}^{\frac{5}{2}}-3x^{\frac{1}{2}}-6x^{\frac{-5}{2}}-20x^{\frac{3}{2}}$

Hence, this is the required solution