Solve x^4x^6+x^5x^5

$$x ^ { 4 } x ^ { 6 } + x ^ { 5 } x ^ { 5 }$$

Evaluate

$$2x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$x^{10}+x^{5}x^{5}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$x^{10}+x^{10}$$

Combine x^{10} and x^{10} to get 2x^{10}.

$$2x^{10}$$

Differentiate w.r.t. x

$$20x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10}+x^{5}x^{5})$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

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

Combine x^{10} and x^{10} to get 2x^{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{10})$$

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

$$10\times 2x^{10-1}$$

Multiply 10 times 2.

$$20x^{10-1}$$

Subtract 1 from 10.

$$20x^{9}$$