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Find the derivative of $\left(2x+3y\right)^2$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\left(2x+3y\right)^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(2\left(x+h\right)+3y\right)^2-\left(2x+3y\right)^2}{h}\right)$
Learn how to solve trigonometric integrals problems step by step online. Find the derivative of (2x+3y)^2 using the definition. Find the derivative of \left(2x+3y\right)^2 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \left(2x+3y\right)^2. Substituting f(x+h) and f(x) on the limit, we get. Expand the expression \left(2\left(x+h\right)+3y\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Expand the expression \left(x+h\right)^{2} using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term 4 by each term of the polynomial \left(x^{2}+2xh+h^{2}\right).