Solve 3x*5x^2-2x^3(-4)

$$3 x \times 5 x ^ { 2 } - 2 x ^ { 3 } ( - 4 )$$

Evaluate

$$23x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3x^{3}\times 5-2x^{3}\left(-4\right)$$

Multiply 3 and 5 to get 15.

$$15x^{3}-2x^{3}\left(-4\right)$$

Multiply 2 and -4 to get -8.

$$15x^{3}-\left(-8x^{3}\right)$$

The opposite of -8x^{3} is 8x^{3}.

$$15x^{3}+8x^{3}$$

Combine 15x^{3} and 8x^{3} to get 23x^{3}.

$$23x^{3}$$

Differentiate w.r.t. x

$$69x^{2}$$

Steps Using Derivative Rule for Sum

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}.

$$15x^{2}x^{1-1}+3\times 8x^{3-1}$$

Subtract 1 from 1.

$$15x^{2}x^{0}+3\times 8x^{3-1}$$

Multiply 3 times -4\left(-2\right).

$$15x^{2}x^{0}+24x^{3-1}$$

Subtract 1 from 3.

$$15x^{2}x^{0}+24x^{2}$$

For any term t except 0, t^{0}=1.

$$15x^{2}\times 1+24x^{2}$$

For any term t, t\times 1=t and 1t=t.

$$15x^{2}+24x^{2}$$