Solve 2x^3(5xy^0)x^3

$$2 x ^ { 3 } ( 5 x y ^ { 0 } ) x ^ { 3 }$$

Evaluate

$$10x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$2x^{4}\times 5y^{0}x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$2x^{7}\times 5y^{0}$$

Multiply 2 and 5 to get 10.

$$10x^{7}y^{0}$$

Calculate y to the power of 0 and get 1.

$$10x^{7}\times 1$$

Multiply 10 and 1 to get 10.

$$10x^{7}$$

Differentiate w.r.t. x

$$70x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 5y^{0}x^{3})$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7}\times 5y^{0})$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{7}y^{0})$$

Calculate y to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{7}\times 1)$$

Multiply 10 and 1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{7})$$

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

$$7\times 10x^{7-1}$$

Multiply 7 times 10.

$$70x^{7-1}$$

Subtract 1 from 7.

$$70x^{6}$$