Solve (3x^{2}+8x^5-10x^2+10x^3)^prime

$$( 3 x ^ { 2 } + 8 x ^ { 5 } - 10 x ^ { 2 } + 10 x ^ { 3 } ) ^ { \prime }$$

Evaluate

$$2x\left(20x^{3}+15x-7\right)$$

Steps Using Derivative Rule for Sum

Combine 3x^{2} and -10x^{2} to get -7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{2}+8x^{5}+10x^{3})$$

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}.

$$2\left(-7\right)x^{2-1}+5\times 8x^{5-1}+3\times 10x^{3-1}$$

Multiply 2 times -7.

$$-14x^{2-1}+5\times 8x^{5-1}+3\times 10x^{3-1}$$

Subtract 1 from 2.

$$-14x^{1}+5\times 8x^{5-1}+3\times 10x^{3-1}$$

Multiply 5 times 8.

$$-14x^{1}+40x^{5-1}+3\times 10x^{3-1}$$

Subtract 1 from 5.

$$-14x^{1}+40x^{4}+3\times 10x^{3-1}$$

Multiply 5 times 8.

$$-14x^{1}+40x^{4}+30x^{3-1}$$

Subtract 1 from 3.

$$-14x^{1}+40x^{4}+30x^{2}$$

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

$$-14x+40x^{4}+30x^{2}$$

Differentiate w.r.t. x

$$160x^{3}+60x-14$$