Solve 3x^5-4/3x^2*3/2x^3=

$$3 x ^ { 5 } - \frac { 4 } { 3 } x ^ { 2 } \cdot \frac { 3 } { 2 } x ^ { 3 } =$$

Evaluate

$$x^{5}$$

Solution Steps

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

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

Multiply \frac{4}{3} and \frac{3}{2} to get 2.

$$3x^{5}-2x^{5}$$

Combine 3x^{5} and -2x^{5} to get x^{5}.

$$x^{5}$$

Differentiate w.r.t. x

$$5x^{4}$$

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}.

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

Multiply 5 times 3.

$$15x^{5-1}+2\left(-\frac{6x^{3}}{3}\right)x^{2-1}$$

Subtract 1 from 5.

$$15x^{4}+2\left(-\frac{6x^{3}}{3}\right)x^{2-1}$$

Multiply 2 times -\frac{4}{3}\times \frac{3}{2}x^{3}.

$$15x^{4}+\left(-4x^{3}\right)x^{2-1}$$

Subtract 1 from 2.

$$15x^{4}+\left(-4x^{3}\right)x^{1}$$

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

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