Solve -512x^17div64x^8=?

$$- 512 x ^ { 17 } \div 64 x ^ { 8 } = ?$$

Evaluate

$$-8x^{25}$$

Solution Steps

Divide -512x^{17} by 64 to get -8x^{17}.

$$-8x^{17}x^{8}$$

To multiply powers of the same base, add their exponents. Add 17 and 8 to get 25.

$$-8x^{25}$$

Differentiate w.r.t. x

$$-200x^{24}$$

Steps Using Definition of a Derivative

Divide -512x^{17} by 64 to get -8x^{17}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{17}x^{8})$$

To multiply powers of the same base, add their exponents. Add 17 and 8 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{25})$$

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

$$25\left(-8\right)x^{25-1}$$

Multiply 25 times -8.

$$-200x^{25-1}$$

Subtract 1 from 25.

$$-200x^{24}$$