Solve (5x^2)(4x^3)-6x^5

$$( 5 x ^ { 2 } ) ( 4 x ^ { 3 } ) - 6 x ^ { 5 }$$

Evaluate

$$14x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$5x^{5}\times 4-6x^{5}$$

Multiply 5 and 4 to get 20.

$$20x^{5}-6x^{5}$$

Combine 20x^{5} and -6x^{5} to get 14x^{5}.

$$14x^{5}$$

Differentiate w.r.t. x

$$70x^{4}$$

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}.

$$2\times 20x^{3}x^{2-1}+5\left(-6\right)x^{5-1}$$

Multiply 2 times 4\times 5x^{3}.

$$40x^{3}x^{2-1}+5\left(-6\right)x^{5-1}$$

Subtract 1 from 2.

$$40x^{3}x^{1}+5\left(-6\right)x^{5-1}$$

Multiply 5 times -6.

$$40x^{3}x^{1}-30x^{5-1}$$

Subtract 1 from 5.

$$40x^{3}x^{1}-30x^{4}$$

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

$$40x^{3}x-30x^{4}$$