Solve (7d^-6)(-4d^-2)/2d^-4

$$\frac { ( 7 d ^ { - 6 } ) ( - 4 d ^ { - 2 } ) } { 2 d ^ { - 4 } }$$

Evaluate

$$-\frac{14}{d^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -2 to get -8.

$$\frac{7d^{-8}\left(-4\right)}{2d^{-4}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-2\times 7d^{-8}}{d^{-4}}$$

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

$$\frac{-2\times 7}{d^{4}}$$

Multiply -2 and 7 to get -14.

$$\frac{-14}{d^{4}}$$

Differentiate w.r.t. d

$$\frac{56}{d^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\left(-\frac{\frac{28}{d^{2}}}{2}\right)d^{-6-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\left(-\frac{14}{d^{2}}\right)d^{-2})$$

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}.

$$-2\left(-\frac{14}{d^{2}}\right)d^{-2-1}$$

Do the arithmetic.

$$\frac{28}{d^{2}}d^{-3}$$