Solve 2x*3x^3+7

$$2 x \cdot 3 x ^ { 3 } + 7$$

Evaluate

$$6x^{4}+7$$

Solution Steps

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

$$2x^{4}\times 3+7$$

Multiply 2 and 3 to get 6.

$$6x^{4}+7$$

Differentiate w.r.t. x

$$24x^{3}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 3+7)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{4}+7)$$

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}.

$$4\times 6x^{4-1}$$

Multiply 4 times 6.

$$24x^{4-1}$$

Subtract 1 from 4.

$$24x^{3}$$