Solve 30x^340x^650x^7

$$30 x ^ { 3 } 40 x ^ { 6 } 50 x ^ { 7 }$$

Evaluate

$$60000x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$30x^{9}\times 40\times 50x^{7}$$

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

$$30x^{16}\times 40\times 50$$

Multiply 30 and 40 to get 1200.

$$1200x^{16}\times 50$$

Multiply 1200 and 50 to get 60000.

$$60000x^{16}$$

Differentiate w.r.t. x

$$960000x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{9}\times 40\times 50x^{7})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{16}\times 40\times 50)$$

Multiply 30 and 40 to get 1200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1200x^{16}\times 50)$$

Multiply 1200 and 50 to get 60000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(60000x^{16})$$

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

$$16\times 60000x^{16-1}$$

Multiply 16 times 60000.

$$960000x^{16-1}$$

Subtract 1 from 16.

$$960000x^{15}$$