Solve 2x^10*(-5x^22)

$$2 x ^ { 10 } \cdot ( - 5 x ^ { 22 } )$$

Evaluate

$$-10x^{32}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 22 to get 32.

$$2x^{32}\left(-5\right)$$

Multiply 2 and -5 to get -10.

$$-10x^{32}$$

Differentiate w.r.t. x

$$-320x^{31}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 22 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{32}\left(-5\right))$$

Multiply 2 and -5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{32})$$

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

$$32\left(-10\right)x^{32-1}$$

Multiply 32 times -10.

$$-320x^{32-1}$$

Subtract 1 from 32.

$$-320x^{31}$$