Solve 7x*6x^2/x^9

$$\frac { 7 x \cdot 6 x ^ { 2 } } { x ^ { 9 } }$$

Evaluate

$$\frac{42}{x^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{7x^{3}\times 6}{x^{9}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{6\times 7}{x^{6}}$$

Multiply 6 and 7 to get 42.

$$\frac{42}{x^{6}}$$

Differentiate w.r.t. x

$$-\frac{252}{x^{7}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{42x^{2}}{1}x^{1-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x^{2}x^{-8})$$

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}.

$$-8\times 42x^{2}x^{-8-1}$$

Do the arithmetic.

$$\left(-336x^{2}\right)x^{-9}$$