Final answer to the problem
$4\left(\sqrt{x^{3}}\sqrt{y^{7}}+x\left(\frac{3}{2}\sqrt{x}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{3}}\sqrt{y^{5}}\right)\right)+3\left(\sqrt{y^{7}}\sqrt{x^{3}}+x\left(2y\sqrt{x^{3}}\sqrt{y^{3}}+y^2\left(\frac{3}{2}\sqrt{x}\sqrt{y^{3}}+\frac{3}{2}\sqrt{x^{3}}\sqrt{y}\right)\right)\right)-7\left(\sqrt{x^{5}}\sqrt{y^{5}}+y\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{5}}+\frac{5}{2}\sqrt{x^{5}}\sqrt{y^{3}}\right)\right)+5\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{5}}\sqrt{y^{5}}\right)$
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Step-by-step Solution
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1
Simplifying
$\frac{d}{dx}\left(4x\sqrt{x^3y^7}+3xy^2\sqrt{x^3y^3}-7y\sqrt{x^5y^5}+\frac{x\sqrt{25x^3y^9}}{y}\right)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(4x\sqrt{x^3y^7}+3xy^2\sqrt{x^3y^3}-7y\sqrt{x^5y^5}+\frac{x\sqrt{25x^3y^9}}{y}\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative of 4x(x^3y^7)^1/2+3xy^2(x^3y^3)^1/2-7y(x^5y^5)^1/2x/y(25x^3y^9)^1/2. Simplifying. The power of a product is equal to the product of it's factors raised to the same power. When multiplying exponents with same base you can add the exponents: 5x\sqrt{x^{3}}\sqrt{y^{9}}. Simplify the fraction \frac{5\sqrt{x^{5}}\sqrt{y^{9}}}{y} by y.
Final answer to the problem
$4\left(\sqrt{x^{3}}\sqrt{y^{7}}+x\left(\frac{3}{2}\sqrt{x}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{3}}\sqrt{y^{5}}\right)\right)+3\left(\sqrt{y^{7}}\sqrt{x^{3}}+x\left(2y\sqrt{x^{3}}\sqrt{y^{3}}+y^2\left(\frac{3}{2}\sqrt{x}\sqrt{y^{3}}+\frac{3}{2}\sqrt{x^{3}}\sqrt{y}\right)\right)\right)-7\left(\sqrt{x^{5}}\sqrt{y^{5}}+y\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{5}}+\frac{5}{2}\sqrt{x^{5}}\sqrt{y^{3}}\right)\right)+5\left(\frac{5}{2}\sqrt{x^{3}}\sqrt{y^{7}}+\frac{7}{2}\sqrt{x^{5}}\sqrt{y^{5}}\right)$