Solve 3x^2+7x^2+5x^2

$$3 x ^ { 2 } + 7 x ^ { 2 } + 5 x ^ { 2 }$$

Evaluate

$$15x^{2}$$

Solution Steps

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

$$10x^{2}+5x^{2}$$

Combine 10x^{2} and 5x^{2} to get 15x^{2}.

$$15x^{2}$$

Differentiate w.r.t. x

$$30x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}+5x^{2})$$

Combine 10x^{2} and 5x^{2} to get 15x^{2}.

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

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

$$2\times 15x^{2-1}$$

Multiply 2 times 15.

$$30x^{2-1}$$

Subtract 1 from 2.

$$30x^{1}$$

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

$$30x$$