Solve 32x^8:4x

$$32 x ^ { 8 } : 4 x$$

Evaluate

$$8x^{9}$$

Solution Steps

Divide 32x^{8} by 4 to get 8x^{8}.

$$8x^{8}x$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$8x^{9}$$

Differentiate w.r.t. x

$$72x^{8}$$

Steps Using Definition of a Derivative

Divide 32x^{8} by 4 to get 8x^{8}.

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

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{9})$$

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

$$9\times 8x^{9-1}$$

Multiply 9 times 8.

$$72x^{9-1}$$

Subtract 1 from 9.

$$72x^{8}$$