Solve 7x^4x^5*(-x^7)

$$7 { x }^{ 4 } { x }^{ 5 } \times (- { x }^{ 7 } )$$

Evaluate

$$-7x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$7x^{9}\left(-x^{7}\right)$$

Multiply 7 and -1 to get -7.

$$-7x^{9}x^{7}$$

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$-7x^{16}$$

Differentiate w.r.t. x

$$-112x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{9}\left(-x^{7}\right))$$

Multiply 7 and -1 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{9}x^{7})$$

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{16})$$

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

$$16\left(-7\right)x^{16-1}$$

Multiply 16 times -7.

$$-112x^{16-1}$$

Subtract 1 from 16.

$$-112x^{15}$$