Solve 2left(x^3right)^5-left(x^5right)^3

$$2 { \left( { x }^{ 3 } \right) }^{ 5 } - { \left( { x }^{ 5 } \right) }^{ 3 }$$

Evaluate

$$x^{15}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$2x^{15}-\left(x^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$2x^{15}-x^{15}$$

Combine 2x^{15} and -x^{15} to get x^{15}.

$$x^{15}$$

Differentiate w.r.t. x

$$15x^{14}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{15}-\left(x^{5}\right)^{3})$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{15}-x^{15})$$

Combine 2x^{15} and -x^{15} to get x^{15}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{15})$$

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

$$15x^{15-1}$$

Subtract 1 from 15.

$$15x^{14}$$