Solve 3x^{3}*x^{9}+x^2*x^10-2x*x^3*x^8

$$3 x ^ { 3 } \cdot x ^ { 9 } + x ^ { 2 } \cdot x ^ { 10 } - 2 x \cdot x ^ { 3 } \cdot x ^ { 8 }$$

Evaluate

$$2x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$3x^{12}+x^{2}x^{10}-2xx^{3}x^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$3x^{12}+x^{12}-2xx^{3}x^{8}$$

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

$$3x^{12}+x^{12}-2x^{4}x^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$3x^{12}+x^{12}-2x^{12}$$

Combine 3x^{12} and x^{12} to get 4x^{12}.

$$4x^{12}-2x^{12}$$

Combine 4x^{12} and -2x^{12} to get 2x^{12}.

$$2x^{12}$$

Differentiate w.r.t. x

$$24x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{12}+x^{2}x^{10}-2xx^{3}x^{8})$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{12}+x^{12}-2xx^{3}x^{8})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{12}+x^{12}-2x^{4}x^{8})$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{12}+x^{12}-2x^{12})$$

Combine 3x^{12} and x^{12} to get 4x^{12}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}-2x^{12})$$

Combine 4x^{12} and -2x^{12} to get 2x^{12}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{12})$$

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

$$12\times 2x^{12-1}$$

Multiply 12 times 2.

$$24x^{12-1}$$

Subtract 1 from 12.

$$24x^{11}$$