Question

If y = x ^ 5 + x ^ 4 + sqrt(x) , find (dy)/(dx
answer step by step​

Answer 1

Answer:

$\frac{dy}{dx}=5x^4+4x^3+\frac{1}{2\sqrt{x}}$

Explanation:

$y=x^5+x^4+\sqrt{x}\\\\\implies y=x^5+x^4+x^{\frac{1}{2} }\\\\\implies \frac{dy}{dx}=\frac{d}{dx}(x^5+x^4+x^{\frac{1}{2} })\\\\\implies\frac{dy}{dx}=\frac{d}{dx}x^5+\frac{d}{dx}x^4+\frac{d}{dx}x^{\frac{1}{2} }\\\\\implies\frac{dy}{dx}=5x^{5-1}+4x^{4-1}+\frac{1}{2}x^{{\frac{1}{2}}-1}\\\\\implies \frac{dy}{dx}=5x^{4}+4x^{3}+\frac{1}{2}x^{{-\frac{1}{2}}}\\\\\implies \frac{dy}{dx}=5x^{4}+4x^{3}+\frac{1}{2\sqrt{x}}$