Solve 56x^15:7x^6=

$$56 x ^ { 15 } : 7 x ^ { 6 } =$$

Evaluate

$$8x^{21}$$

Solution Steps

Divide 56x^{15} by 7 to get 8x^{15}.

$$8x^{15}x^{6}$$

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$8x^{21}$$

Differentiate w.r.t. x

$$168x^{20}$$

Steps Using Definition of a Derivative

Divide 56x^{15} by 7 to get 8x^{15}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{15}x^{6})$$

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{21})$$

The derivative of ax^{n} is nax^{n-1}.

$$21\times 8x^{21-1}$$

Multiply 21 times 8.

$$168x^{21-1}$$

Subtract 1 from 21.

$$168x^{20}$$