Solve 4x^4*3x^6-1

$$4 x ^ { 4 } \cdot 3 x ^ { 6 } - 1$$

Evaluate

$$12x^{10}-1$$

Solution Steps

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

$$4x^{10}\times 3-1$$

Multiply 4 and 3 to get 12.

$$12x^{10}-1$$

Differentiate w.r.t. x

$$120x^{9}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{10}\times 3-1)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{10}-1)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$10\times 12x^{10-1}$$

Multiply 10 times 12.

$$120x^{10-1}$$

Subtract 1 from 10.

$$120x^{9}$$