Solve 6*x^5*(-1/2)*x^4

$$6 \cdot x ^ { 5 } \cdot ( - \frac { 1 } { 2 } ) \cdot x ^ { 4 }$$

Evaluate

$$-3x^{9}$$

Solution Steps

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

$$6x^{9}\left(-\frac{1}{2}\right)$$

Multiply 6 and -\frac{1}{2} to get -3.

$$-3x^{9}$$

Differentiate w.r.t. x

$$-27x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{9}\left(-\frac{1}{2}\right))$$

Multiply 6 and -\frac{1}{2} to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{9})$$

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

$$9\left(-3\right)x^{9-1}$$

Multiply 9 times -3.

$$-27x^{9-1}$$

Subtract 1 from 9.

$$-27x^{8}$$