Solve 6x^{3}+8x^2+4x^3-10x^3+15x^2

$$6 x ^ { 3 } + 8 x ^ { 2 } + 4 x ^ { 3 } - 10 x ^ { 3 } + 15 x ^ { 2 }$$

Evaluate

$$23x^{2}$$

Solution Steps

Combine 6x^{3} and 4x^{3} to get 10x^{3}.

$$10x^{3}+8x^{2}-10x^{3}+15x^{2}$$

Combine 10x^{3} and -10x^{3} to get 0.

$$8x^{2}+15x^{2}$$

Combine 8x^{2} and 15x^{2} to get 23x^{2}.

$$23x^{2}$$

Differentiate w.r.t. x

$$46x$$

Steps Using Definition of a Derivative

Combine 6x^{3} and 4x^{3} to get 10x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{3}+8x^{2}-10x^{3}+15x^{2})$$

Combine 10x^{3} and -10x^{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2}+15x^{2})$$

Combine 8x^{2} and 15x^{2} to get 23x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(23x^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 23x^{2-1}$$

Multiply 2 times 23.

$$46x^{2-1}$$

Subtract 1 from 2.

$$46x^{1}$$

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

$$46x$$