Solve S(t)=203.6t+38,230^7

$$S ( t ) = 203.6 t + 38,230 ^ { 7 }$$

Differentiate w.r.t. t

$$203.6$$

Steps Using Derivative Rule for Sum

Calculate 38230 to the power of 7 and get 119352105857070471307928470000000.

$$\frac{\mathrm{d}}{\mathrm{d}t}(203.6t+119352105857070471307928470000000)$$

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}.

$$203.6t^{1-1}$$

Subtract 1 from 1.

$$203.6t^{0}$$

For any term t except 0, t^{0}=1.

$$203.6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$203.6$$

Evaluate

$$\frac{1018t}{5}+119352105857070471307928470000000$$

Solution Steps

Calculate 38230 to the power of 7 and get 119352105857070471307928470000000.

$$203.6t+119352105857070471307928470000000$$