Solve 26x^16*23x^33

$$26 x ^ { 16 } \cdot 23 x ^ { 33 }$$

Evaluate

$$598x^{49}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 16 and 33 to get 49.

$$26x^{49}\times 23$$

Multiply 26 and 23 to get 598.

$$598x^{49}$$

Differentiate w.r.t. x

$$29302x^{48}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 16 and 33 to get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26x^{49}\times 23)$$

Multiply 26 and 23 to get 598.

$$\frac{\mathrm{d}}{\mathrm{d}x}(598x^{49})$$

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

$$49\times 598x^{49-1}$$

Multiply 49 times 598.

$$29302x^{49-1}$$

Subtract 1 from 49.

$$29302x^{48}$$