Question
Diffrentiate the following w.r.t.x
$\log \left[\cos \left(x^3-5\right)\right]$
✓
Answer
Let $y=\log \left[\cos \left(x^3-5\right)\right]$
Differentiating w.r.t. x, we get
$\frac{d y}{d x}=\frac{d}{d x}\left\{\log \left[\cos \left(x^3-5\right)\right]\right\}$
$\begin{aligned} & =\frac{1}{\cos \left(x^3-5\right)} \cdot \frac{d}{d x}\left[\cos \left(x^3-5\right)\right] \\ & =\frac{1}{\cos \left(x^3-5\right)} \cdot\left[-\sin \left(x^3-5\right)\right] \cdot \frac{d}{d x}\left(x^3-5\right) \\ & =-\tan \left(x^3-5\right) \times\left(3 x^2-0\right) \\ & =-3 x^2 \tan \left(x^3-5\right) .\end{aligned}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
if f(1) = 4, f'(1) = 2, find the value of the derivative of $\log\Big(\text{f}\big(\text{e}^\text{x}\big)\Big)$ w.r.t x at the point x = 0.
→Which one of the following graphs represents a function?
Write the value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{k}}\times\hat{\text{i}}\big)+\hat{\text{k}}.\big(\hat{\text{i}}\times\hat{\text{j}}\big).$
→Find the condition that the line $4x + 5y = 0$ coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$
→There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?
Write two different vectors having same magnitude.
Find the vector equation of a plane which is at a distance of 5 unit from the origin and which is normal to the vector $\hat{\text{i}}-2\hat{\text{j}}-2\hat{\text{k}}$
→Evaluate: $\int_0^{\frac{\pi}{2}} \frac{\sin ^2 x}{(1+\cos x)^2} d x$
→Evaluate :
→$\int_{-\pi / 4}^{\pi / 4} x^3 \cdot \sin ^4 x \cdot d x$
Evaluate:
$\cos\Big(\sec^{-1}\text{x}+\text{cosec}^{-1}\text{x}\Big)$
→$\cos\Big(\sec^{-1}\text{x}+\text{cosec}^{-1}\text{x}\Big)$