Solve -512x^217div64x^8

$$-512 { x }^{ 217 } \div 64 { x }^{ 8 }$$

Evaluate

$$-8x^{225}$$

Solution Steps

Divide -512x^{217} by 64 to get -8x^{217}.

$$-8x^{217}x^{8}$$

To multiply powers of the same base, add their exponents. Add 217 and 8 to get 225.

$$-8x^{225}$$

Differentiate w.r.t. x

$$-1800x^{224}$$

Steps Using Definition of a Derivative

Divide -512x^{217} by 64 to get -8x^{217}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{217}x^{8})$$

To multiply powers of the same base, add their exponents. Add 217 and 8 to get 225.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{225})$$

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

$$225\left(-8\right)x^{225-1}$$

Multiply 225 times -8.

$$-1800x^{225-1}$$

Subtract 1 from 225.

$$-1800x^{224}$$