Solve d/dxleft(3x^2-2/x-5right)6

$$\frac{d}{d x } \left( \frac{ 3 { x }^{ 2 } -2 }{ x-5 } \right) 6$$

Evaluate

$$\frac{6\left(3x^{2}-30x+2\right)}{\left(x-5\right)^{2}}$$

Steps Using Derivative Rule for Quotient

Express \frac{3x^{2}-2}{x-5}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(3x^{2}-2\right)\times 6}{x-5})$$

Use the distributive property to multiply 3x^{2}-2 by 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x^{2}-12}{x-5})$$

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.

$$\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(18x^{2}-12)-\left(18x^{2}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}}$$

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}.

$$\frac{\left(x^{1}-5\right)\times 2\times 18x^{2-1}-\left(18x^{2}-12\right)x^{1-1}}{\left(x^{1}-5\right)^{2}}$$

Do the arithmetic.

$$\frac{\left(x^{1}-5\right)\times 36x^{1}-\left(18x^{2}-12\right)x^{0}}{\left(x^{1}-5\right)^{2}}$$

Expand using distributive property.

$$\frac{x^{1}\times 36x^{1}-5\times 36x^{1}-\left(18x^{2}x^{0}-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{36x^{1+1}-5\times 36x^{1}-\left(18x^{2}-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Do the arithmetic.

$$\frac{36x^{2}-180x^{1}-\left(18x^{2}-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Remove unnecessary parentheses.

$$\frac{36x^{2}-180x^{1}-18x^{2}-\left(-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Combine like terms.

$$\frac{\left(36-18\right)x^{2}-180x^{1}-\left(-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Subtract 18 from 36.

$$\frac{18x^{2}-180x^{1}-\left(-12x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{18x^{2}-180x-\left(-12x^{0}\right)}{\left(x-5\right)^{2}}$$

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

$$\frac{18x^{2}-180x-\left(-12\right)}{\left(x-5\right)^{2}}$$

Differentiate w.r.t. x

$$\frac{876}{\left(x-5\right)^{3}}$$