Solve x^2*x^4+(x^3)^2*6

$$x ^ { 2 } \cdot x ^ { 4 } + ( x ^ { 3 } ) ^ { 2 } \cdot 6$$

Evaluate

$$7x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$x^{6}+\left(x^{3}\right)^{2}\times 6$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}+x^{6}\times 6$$

Combine x^{6} and x^{6}\times 6 to get 7x^{6}.

$$7x^{6}$$

Differentiate w.r.t. x

$$42x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}+\left(x^{3}\right)^{2}\times 6)$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}+x^{6}\times 6)$$

Combine x^{6} and x^{6}\times 6 to get 7x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{6})$$

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

$$6\times 7x^{6-1}$$

Multiply 6 times 7.

$$42x^{6-1}$$

Subtract 1 from 6.

$$42x^{5}$$