Evaluate
\frac{36x^{4}-15x^{3}-41x^{2}-10x+7}{3x+2}
Differentiate w.r.t. x
\frac{324x^{4}+198x^{3}-213x^{2}-164x-41}{\left(3x+2\right)^{2}}
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\frac{\left(12x^{3}-13x^{2}-5x\right)\left(3x+2\right)}{3x+2}+\frac{7}{3x+2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 12x^{3}-13x^{2}-5x times \frac{3x+2}{3x+2}.
\frac{\left(12x^{3}-13x^{2}-5x\right)\left(3x+2\right)+7}{3x+2}
Since \frac{\left(12x^{3}-13x^{2}-5x\right)\left(3x+2\right)}{3x+2} and \frac{7}{3x+2} have the same denominator, add them by adding their numerators.
\frac{36x^{4}+24x^{3}-39x^{3}-26x^{2}-15x^{2}-10x+7}{3x+2}
Do the multiplications in \left(12x^{3}-13x^{2}-5x\right)\left(3x+2\right)+7.
\frac{36x^{4}-15x^{3}-41x^{2}-10x+7}{3x+2}
Combine like terms in 36x^{4}+24x^{3}-39x^{3}-26x^{2}-15x^{2}-10x+7.
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