Solve d/dxleft(4*3x^2-2/x-5right)

$$\frac{d}{d x } \left( \frac{ 4 \times 3 { x }^{ 2 } -2 }{ x-5 } \right)$$

Evaluate

$$\frac{2\left(6x^{2}-60x+1\right)}{\left(x-5\right)^{2}}$$

Steps Using Derivative Rule for Quotient

Multiply 4 and 3 to get 12.

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

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.

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

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}.

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

Do the arithmetic.

$$\frac{\left(x^{1}-5\right)\times 24x^{1}-\left(12x^{2}-2\right)x^{0}}{\left(x^{1}-5\right)^{2}}$$

Expand using distributive property.

$$\frac{x^{1}\times 24x^{1}-5\times 24x^{1}-\left(12x^{2}x^{0}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{24x^{1+1}-5\times 24x^{1}-\left(12x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Do the arithmetic.

$$\frac{24x^{2}-120x^{1}-\left(12x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Remove unnecessary parentheses.

$$\frac{24x^{2}-120x^{1}-12x^{2}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Combine like terms.

$$\frac{\left(24-12\right)x^{2}-120x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Subtract 12 from 24.

$$\frac{12x^{2}-120x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{12x^{2}-120x-\left(-2x^{0}\right)}{\left(x-5\right)^{2}}$$

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

$$\frac{12x^{2}-120x-\left(-2\right)}{\left(x-5\right)^{2}}$$

Differentiate w.r.t. x

$$\frac{596}{\left(x-5\right)^{3}}$$