Solve 30t^{3}+(-5t^3)+9t^3-17t^3-(-8t^3)

$$30 t ^ { 3 } + ( - 5 t ^ { 3 } ) + 9 t ^ { 3 } - 17 t ^ { 3 } - ( - 8 t ^ { 3 } )$$

Evaluate

$$25t^{3}$$

Solution Steps

Combine 30t^{3} and -5t^{3} to get 25t^{3}.

$$25t^{3}+9t^{3}-17t^{3}-\left(-8t^{3}\right)$$

Combine 25t^{3} and 9t^{3} to get 34t^{3}.

$$34t^{3}-17t^{3}-\left(-8t^{3}\right)$$

Combine 34t^{3} and -17t^{3} to get 17t^{3}.

$$17t^{3}-\left(-8t^{3}\right)$$

The opposite of -8t^{3} is 8t^{3}.

$$17t^{3}+8t^{3}$$

Combine 17t^{3} and 8t^{3} to get 25t^{3}.

$$25t^{3}$$

Differentiate w.r.t. t

$$75t^{2}$$

Steps Using Definition of a Derivative

Combine 30t^{3} and -5t^{3} to get 25t^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(25t^{3}+9t^{3}-17t^{3}-\left(-8t^{3}\right))$$

Combine 25t^{3} and 9t^{3} to get 34t^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(34t^{3}-17t^{3}-\left(-8t^{3}\right))$$

Combine 34t^{3} and -17t^{3} to get 17t^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(17t^{3}-\left(-8t^{3}\right))$$

The opposite of -8t^{3} is 8t^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(17t^{3}+8t^{3})$$

Combine 17t^{3} and 8t^{3} to get 25t^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(25t^{3})$$

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

$$3\times 25t^{3-1}$$

Multiply 3 times 25.

$$75t^{3-1}$$

Subtract 1 from 3.

$$75t^{2}$$