Solve d/dxleft(3x^2-2/x-5right)86931

$$\frac{d}{d x } \left( \frac{ 3 { x }^{ 2 } -2 }{ x-5 } \right) 86931$$

Evaluate

$$\frac{86931\left(3x^{2}-30x+2\right)}{\left(x-5\right)^{2}}$$

Steps Using Derivative Rule for Quotient

Express \frac{3x^{2}-2}{x-5}\times 86931 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(3x^{2}-2\right)\times 86931}{x-5})$$

Use the distributive property to multiply 3x^{2}-2 by 86931.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{260793x^{2}-173862}{x-5})$$

For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.

$$\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(260793x^{2}-173862)-\left(260793x^{2}-173862\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}}$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{\left(x^{1}-5\right)\times 2\times 260793x^{2-1}-\left(260793x^{2}-173862\right)x^{1-1}}{\left(x^{1}-5\right)^{2}}$$

Do the arithmetic.

$$\frac{\left(x^{1}-5\right)\times 521586x^{1}-\left(260793x^{2}-173862\right)x^{0}}{\left(x^{1}-5\right)^{2}}$$

Expand using distributive property.

$$\frac{x^{1}\times 521586x^{1}-5\times 521586x^{1}-\left(260793x^{2}x^{0}-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

To multiply powers of the same base, add their exponents.

$$\frac{521586x^{1+1}-5\times 521586x^{1}-\left(260793x^{2}-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Do the arithmetic.

$$\frac{521586x^{2}-2607930x^{1}-\left(260793x^{2}-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Remove unnecessary parentheses.

$$\frac{521586x^{2}-2607930x^{1}-260793x^{2}-\left(-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Combine like terms.

$$\frac{\left(521586-260793\right)x^{2}-2607930x^{1}-\left(-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Subtract 260793 from 521586.

$$\frac{260793x^{2}-2607930x^{1}-\left(-173862x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

For any term t, t^{1}=t.

$$\frac{260793x^{2}-2607930x-\left(-173862x^{0}\right)}{\left(x-5\right)^{2}}$$

For any term t except 0, t^{0}=1.

$$\frac{260793x^{2}-2607930x-\left(-173862\right)}{\left(x-5\right)^{2}}$$

Differentiate w.r.t. x

$$\frac{12691926}{\left(x-5\right)^{3}}$$