Solve 1/1-6:x^2

$$\frac { 1 } { 1 - 6 } : x ^ { 2 }$$

Evaluate

$$-\frac{1}{5x^{2}}$$

Solution Steps

Express \frac{\frac{1}{1-6}}{x^{2}} as a single fraction.

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

Subtract 6 from 1 to get -5.

$$\frac{1}{-5x^{2}}$$

Differentiate w.r.t. x

$$\frac{2}{5x^{3}}$$

Steps Using Chain Rule

Express \frac{\frac{1}{1-6}}{x^{2}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\left(1-6\right)x^{2}})$$

Subtract 6 from 1 to get -5.

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

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Simplify.

$$10x^{1}\left(-5x^{2}\right)^{-2}$$

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

$$10x\left(-5x^{2}\right)^{-2}$$