Solve d/dxleft(3x^4^1+5x^3-2x^2right)

$$\frac{d}{d x } \left(3 { x }^{ { 4 }^{ 1 } } +5 { x }^{ 3 } -2 { x }^{ 2 } \right)$$

Evaluate

$$x\left(12x^{2}+15x-4\right)$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 1 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{4}+5x^{3}-2x^{2})$$

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}.

$$4\times 3x^{4-1}+3\times 5x^{3-1}+2\left(-2\right)x^{2-1}$$

Multiply 4 times 3.

$$12x^{4-1}+3\times 5x^{3-1}+2\left(-2\right)x^{2-1}$$

Subtract 1 from 4.

$$12x^{3}+3\times 5x^{3-1}+2\left(-2\right)x^{2-1}$$

Multiply 3 times 5.

$$12x^{3}+15x^{3-1}+2\left(-2\right)x^{2-1}$$

Subtract 1 from 3.

$$12x^{3}+15x^{2}+2\left(-2\right)x^{2-1}$$

Multiply 3 times 5.

$$12x^{3}+15x^{2}-4x^{2-1}$$

Subtract 1 from 2.

$$12x^{3}+15x^{2}-4x^{1}$$

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

$$12x^{3}+15x^{2}-4x$$

Differentiate w.r.t. x

$$36x^{2}+30x-4$$